2020-2024 |
Locally Maximal Attractors of Expanding Dynamical Systems. (Ukrainian), Ukrains’kyi Matematychnyi Zhurnal, vol. 76, no. 1, 2024, 17–30 (with V. S. Bondarchuk, A. G. Sivak). DOI:https://doi.org/10.3842/umzh.v76i1.7928 Descriptive Theory of Deterministic Chaos. (English), Ukrains’kyi Matematychnyi Zhurnal, vol. 74, no. 12, 2023, 1950–1960. Descriptive theory of determined chaos. (Ukrainian), Ukrains’kyi Matematychnyi Zhurnal, vol. 74, no. 12, 2023, 1709-1718. Asymptotic Properties of the Semigroup Generated by a Continuous Interval Map., International Journal of Mathematical, Engineering, Biological and Applied Computing, 1 (2), 2022, 77–94 (with O.Yu.Romanenko). Computer Turbulence as a Tunnelling Effect., Journal of Mathematical Sciences, 256 (7), 2021, 703–712 (with E.Yu.Romanenko, A.A.Akbergenov).
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2010-2019 |
Basins of attractors of trajectories, J. Difference Equations and Appl., 22, no. 2, 2016, 159-163 (with Sivak A.G.). On a class of functional and differential functional equations, J. Difference Equations and Appl., 22, no. 1, 2016, 147-157 (with Akbergenov A.A.). On the history of one-dimensional dynamics, J. ESAIM: Proceedings and Surveys, 46, November 2014, 81-83 (Proc. ECIT 2012). To the theory of difference equations with continuous time, in Method of invariants in theory of functional equations (G.P.Pelyukh, A.N.Sharkovsky; Russian), Proc. Inst. Math. NAS Ukraine, vol. 95, Kyiv, 2013, 212-253 (with Romanenko E.Yu.). Ideal turbulence phenomenon and transmission line with Chua's diode, Chapter 16 in Chaos, CNN, Memristors and Beyond, World Scientific, 2013, 202-210 (with Romanenko E.Yu.). Homoclinic trajectories in one-dimensional dynamics, J. Difference Equations and Appl., 18, no. 4, 2012, 579-588 (with Fedorenko, V.V.). Whether Chaos can be achieved in Piecewise Linear Boundary Value Problems, J. Difference Equations & Dynamical Systems, 18, no. 1-2, 2010, 1-9 (with Romanenko E.Yu.). On the Coexistence of Homoclinic and Periodic Trajectories, Nonlinear Dynamics (Russian Sci. J.), 6, no. 1, 2010, 207-217 (with Fedorenko V.V.). Difference Equations and Nonlinear Boundary Problems for Hyperbolic Systems, Discrete dynamics and difference equations (Proceed. ICDEA 2007, Lisbon, Portugal), World Scientific, 2010, 404-409 (with Severino R., Vinagre S.). Difference Equations with Continuous Time: Theory and Applications, Discrete dynamics and difference equations (Proceed. ICDEA 2007, Lisbon, Portugal), World Scientific, 2010, 104-119 (with Romanenko E.Yu.).
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2000-2009 |
Piecewise Linear Boundary Value Problems, Grazer Math. Berichte, 354, 2009, 237-253 (with Romanenko E.Yu.). Sharkovsky ordering. Scholarpedia, 2008, 3(5):1680. Common Periodic Trajectories of Interval Maps, J. Fixed Point Theory Appl., 3, no. 1, 2008, 57-62 (with Matviichuk M.Yu.). One-Dimensional Dynamics and Winnerless Competition of Patterns, 3rd Intern. Conf. "Physics and Control" (PhysCon 2007), Potsdam, Germany, Sept. 3-7, 2007. Dynamical Systems, Encyclopediya Suchasnoi Ukrainy, 7, 2007. The Theory of Dynamical Systems and its Impact on Teaching Mathematics, Suchasna matematyka i matematychna osvita. Zdobytky, problemy, perspectyvy, Dragomanov Univ. Publ., Kyiv, 2007, 59-71. Trajectories of Intervals in One-dimensional Dynamical Systems, J. Difference Equations and Appl., 13, no. 8-9, 2007, 821-828 (with Fedorenko V.V., Romanenko E.Yu.). Computing Topological Invariants in Boundary Value Problems Reducible to Difference Equations, Proceed. Intern. Conf. "Difference equations, special functions and ortogonal polynomials", Munich, Germany, 25-30 July 2005, World Scientific, 2007, 741-751 (with Severino R., Sousa Ramos J., Vinagre S.). Ideal Turbulence and Problems of its Visualization, Proceed. Intern. Conf. "Difference equations, special functions and ortogonal polynomials", Munich, Germany, 25-30 July 2005, World Scientific, 2007, 617-635. Dynamical Systems and Turbulence Modeling, Ukrain. Mat. Zh., 59, 2007, no. 2, 217-230 (with Romanenko E.Yu.). Symbolic dynamics in boundary value problem for systems with two spatial variables, Grazer Math. Berichte, 350, 2006, 210-224 (with Severino R., Sousa Ramos J., Vinagre S.). Topological Invariants in a Model of a Time-Delayed Chua's Circuit, Nonlinear Dynamics, 44, 2006, 81-90 (with Severino R., Sousa Ramos J., Vinagre S.). Ideal turbulence, Nonlinear Dynamics, 44, 2006, 15-27. One-dimensional bifurcations in some infinite-dimensional dynamical systems and ideal turbulence, Regular and chaotic dynamics, 11, no. 2, 2006, 319-328 (with Fedorenko V.V., Romanenko E.Yu.). One-dimensional maps, "Encyclopedia of Nonlinear Science" (ed. Alwyn Scott), Routledge, New York and London, 2005, 665-668 (with Fedorenko, V.V.). Turbulence, ideal, "Encyclopedia of Nonlinear Science" (ed. Alwyn Scott), Routledge, New York and London, 2005, 955-957 (with Romanenko, E.Yu.). Attractors of one-dimensional maps generated by boundary value problems, Second Intern. Conference "Physics and Control", St. Petersburg, August 24-26, 2005, 600-601 (with Sousa Ramos, J., Berezovsky, S.A.). Ideal turbulence and bifurcations in infinite-dimensional dynamical systems, Second Intern. Conference "Physics and Control", St.Petersburg, August 24-26, 2005, 216-219 (with Fedorenko, V.V.). Difference equations and boundary value problems, New Progress in Difference Equations, Proc. ICDEA'2001, Taylor & Francis, London, 2004, 3-22. Difference equations and dynamical systems generated by some classes of boundary value problems, Proceedings of the Steklov Institute of Mathematics, v. 244, Moscow, 2004, 264-279 (with Romanenko, E.Yu.). One-dimensional dynamics generated by boundary value problems for the wave equation, Proc. ECIT'02, Grazer Math. Berichte, Nr 346, 2004, 255-270 (with Lozi, R., Sousa Ramos, J.). Symbolic dynamics in boundary value problems, Proc. ECIT'02, Grazer Math. Berichte, Nr 346, 2004, 393-402 (with Severino, R.,Sousa Ramos, J., Vinagre, S.). Ideal Turbulence: Definition, Proc. ECIT'02, Grazer Math. Berichte, Nr 346, 2004, 403-412. Ideal Turbulence, Proc. Intern. Conf. "Nonlinear Dynamics of Electronic Systems" (9-13 May, 2004, Evora, Portugal), 2004, 34-41. Topological invariants in a model of a time-delayed Chua's circuit, Proc. Intern. Conf. "Nonlinear Dynamics of Electronic Systems" (9-13 May, 2004, Evora, Portugal), 2004, 312-315 (with Severino, R., Sousa Ramos, J., Vinagre, S.). Dynamical systems generated by boundary problems. Ideal Turbulence. Computer Turbulence, Pratsi Ukrainskogo matematychnogo kongresu, Dynamichni systemy, 2003, 125-149. Phase transitions in correct-incorrect calculations for some evolution problems, Intern. J. Bifurcation and Chaos 13, 2003, 1811-1821 (with Berezovsky, S.A.). Ideal Turbulence: Definition and Models, Proc. Intern. Conf. "Physics and Control" (20-22 August, 2003), Petersburg, Russia, 2003, 23-30 (with Romanenko, E.Yu., Berezovsky, S.A.). About calculating the thermal regime of solidation with the consideration of crystallization, Dopovidi NAN Ukrainy, 12, 2002, 7-11 (with Berezovsky, A.A., Berezovsky, S.A., Feldman E.P., Yurchenko V.M.). Asymptotic discontinuity of smooth solutions of nonlinear q-difference equations (Russian), Ukrain. Mat. Zh. 52, 2000, no. 12, 1615-1629 (with Derfel, G.; Romanenko, E.). Long-time properties of solutions of simplest nonlinear q-difference equations, J. Difference Equations and Applications 6, 2000, no. 5, 485-511 (with Derfel, G.; Romanenko, E.). Dido's functional equation revisited (Dedicated to Professor Zenon Moszner on the occasion of his seventieth birthday), Rocznik Nauk.-Dydakt. Prace Mat., no. 17, Krakow, 2000, 143-150 (with Kahlig, Peter; Matkowski, Janusz). Asymptotic behaviour of solutions of simplest nonlinear q-difference equations, Proc. 7th Intern. Conf. on Functional Equations and Inequalities (Zlocki, 1999), Prace Matematyczne, Krakow, 2000 (with Derfel, G.; Romanenko, E.). Recovering trajectories of chaotic piecewise linear systems, Proc. 2nd Intern. Conf. "Control of Oscillations and Chaos" (COC'2000), vol. 2, St.Petersburg, Russia, 2000, 380-383 (with Fedorenko, A. D.; Aziz-Alaoui, M.A..; Lozi R.). Transitions of "correct-incorrect" numerical calculations for solutions of some problems. "Phase transitions" in computer turbulence, Proc. 2nd Intern. Conf. "Control of Oscillations and Chaos" (COC'2000), vol. 1, St.Petersburg, Russia, 2000, 6-9 (with Berezovsky, S. A.).
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1990-1999 |
Dynamics of the solutions of simplest nonlinear boundary value problems (Ukrainian), Ukrain. Mat. Zh. 51, 1999, no. 6, 810-826; translation in Ukrainian Math. J. 51, 1999, no. 6, 907-925 (with Romanenko, E. Yu.). From boundary value problems to difference equations: a method of investigation of chaotic vibrations, Intern. J. Bifurcation and Chaos 9, 1999, no. 7, 1285-1306 (with Romanenko, E. Yu.). Asymptotic properties of solutions of a class of boundary value problems (Ukrainian), Dopovidi Nats. Akad. Nauk Ukrainy, Matem. Prirodozn. Tekh. Nauky, 1999, no. 3, 43-48 (with Romanenko, O. Yu.). Iteration of continuous functions and dynamics of solutions for some boundary value problems, European Conference on Iteration Theory (Muszyna-Zlockie, 1998), Ann. Math. Siles., 1999, no. 13 , 243-255. Computer Turbulence, Proc. Intern. Conf. "Self-similar systems" (Dubna, 1998), Joint Inst. Nuclear Researchs, Dubna, 1999, 251-259 (with Berezovsky, S. A.). Self-structuring and self-stochasticity in difference equations and some boundary value problems, Proc. Intern. Conf. "Self-similar systems" (Dubna, 1998), Joint Inst. Nuclear Researchs, Dubna, 1999, 237-250 (with Vereikina, M. B.; Romanenko, E. Yu.). Continuous dependence on singular parameters in a neutral differential equation, Proc. Intern. Sci. Conf. on Mathematics (Zilina, Slovakia, 1998), Zilina Univ., 1998, 97-103 (with Ivanov, A. F.). Self-stochasticity in deterministic boundary value problems, Nonlinear Boundary Value Problems 9, Inst. Appl. Math.and Mech., NAS of Ukraine, Donetsk, 1998, 174-184 (with Vereikina, M. B.; Romanenko, E. Yu.). Solution behaviour in a class of difference-differential equations, Bull. Austral. Math. Soc. 57, 1998, no. 1, 37-48 (with Fedorenko, A. D.; Fedorenko, V. V.; Ivanov, A. F.). An information signal transmission method by chaotic systems, Nats. Akad. Nauk Ukrainy, Inst. Mat. Preprint 1998, no. 4, 12 pp. (with Fedorenko, A. D.). Shadowing property of dynamical systems and stability of orbit prolongations, Ukrainian Math. J. 49, 1997, no. 8, 1016-1024 (with Vereikina, M. B.). Structural turbulence in boundary value problems, Proc. First Intern. Conf. "Control of Oscillations and Chaos", vol. 3, St.Petersburg, Russia, 1997, 492-497 (with Vereikina, M. B.; Romanenko, E. Yu.). Recovering trajectories of chaotic piecewise linear dynamical systems, Proc. First Intern. Conf. "Control of Oscillations and Chaos", vol. 2, St.Petersburg, Russia, 1997, 230-233 (with Fedorenko, A. D.; Aziz-Alaoui, M.A..; Lozi R.). Coexistence of periodic orbits for a class of discontinuous mappings (Ukrainian), Dopovidi Nation. Akad. Nauk Ukrainy, 1996, no. 11, 21-25 (1997) (with Ivanov, A. F.; Fedorenko, V. V.; Fedorenko, O. D.). From one-dimensional to infinite-dimensional dynamical systems: Ideal turbulence (Ukrainian) (Translated in English), Ukrain. Mat. Zh. 48, 1996, no. 12, 1604-1627; translation in Ukrainian Math. J. 48, 1996, no. 12, 1817-1842 (with Romanenko, E. Yu.). Farey tree for stable periodic waves in a transmission line, CADSEM Preprint N 96-008, 1996, Deakin University (with Ivanov, A. F.; Fedorenko, V. V.; Fedorenko, A. D.). From One-Dimensional to Infinite-Dimensional Dynamical Systems, Proc. of the 3rd Intern. specialist workshop on Nonlinear Dynamics of Electronic Systems (NDES'95) (Dublin, Ireland), 1995, 3-11. Self-Stochasticity in Dynamical Systems as a Scenario for Deterministic Spatio-Temporal Chaos, Chaos and Nonlinear Mechanics, Ser.B, 4, 1995, 172-181 (with Romanenko, E. Yu.). Universal phenomena in some infinite-dimensional dynamical systems, Intern. J. Bifurcation and Chaos 5, 1995, no. 5, 1419-1425; Reprint of the paper in World Sci. Ser. Nonlinear Sci. Ser. B, 8, Thirty years after Sharkovskii's theorem: new perspectives (Murcia, 1994), 1995, 157-163. Self-structuring and self-similarity in boundary value problems, Intern. J. Bifurcation and Chaos 5, 1995, no. 5, 1407-1418; Reprint of the paper in World Sci. Ser. Nonlinear Sci. Ser. B, 8, Thirty years after Sharkovskii's theorem: new perspectives (Murcia, 1994), 1995, 145-156 (with Vereikina, M. B.; Romanenko, E. Yu.). Dry turbulence and period-adding phenomena from a 1-D map with time delay, Intern. J. Bifurcation and Chaos 5, 1995, no. 5, 1283-1302; Reprint of the paper in World Sci. Ser. Nonlinear Sci. Ser. B, 8, Thirty years after Sharkovskii's theorem: new perspectives (Murcia, 1994), 1995, 21-40 (with Deregel, Ph.; Chua, L. O). Coexistence of cycles of a continuous map of the line into itself [Translation from Ukrain. Mat. Zh. 16 (1964), no. 1, 61-71], Intern. J. Bifurcation and Chaos 5, 1995, no. 5, 1263-1273; Reprint of the paper in World Sci. Ser. Nonlinear Sci. Ser. B, 8, Thirty years after Sharkovskii's theorem: new perspectives (Murcia, 1994), 1995, 1-11. Universal phenomena in solution bifurcations of some boundary value problems, J. Nonlinear Math. Phys. 1, 1994, no. 2, Kyiv, 147-157 (with Sivak, Andrij). Ideal turbulence in an idealized time-delayed Chua's circuit, Intern. J. Bifurcation and Chaos 4, 1994, no. 2, 303-309. Oscillations in singularly perturbed delay equations, Dynamics reported: Expositions in dynamical systems 1, Springer, Berlin, 1992, 164-224 (with Ivanov, A.F.). Chaos in some 1-D discontinuous maps that appear in the analysis of electrical circuits,IEEE Transaction On Circuits and Systems I, 1993, no. 40 (10) (with Chua L.O.). Chaos from a time-delayed Chua's circuit, IEEE Transaction on Circuits and Systems I, 1993, 40(10). Dry turbulence from a time-delayed Chua's circuit, J. of Circuits, Systems and Computers, 1993, 3(2) (with Maistrenko Yu., Deregel Ph., Chua L.O.). Autostochasticity: attractors of deterministic problems can contain random functions (Russian), Dokl. Akad. Nauk Ukrainy, 1992, no. 10, 33-37 (with Romanenko, E. Yu.). Ideal turbulence: attractors of deterministic systems may lie in the space of random fields, Intern. J. Bifurcation and Chaos 2, 1992, no. 1, 31-36 (with Romanenko, E. Yu.). Problems of turbulence theory and iteration theory, Proc. European Conf. Iteration Theory (ECIT-91), World Sci. Publ., Singapore, 1992, 242-252 (with Romanenko, E.Yu.). On Newton's method (Ukrainian), U sviti matematyki [In the World of Mathematics] 20, Radianska shkola, Kyiv, 1991, 18-31 (with Ivanov, A. F.). On topological dynamics of triangular maps of the plane, Proc. European Conf. Iteration Theory (ECIT-1989), World Sci. Publ., Singapore, 1991, 177-183 (with Kolyada, S. F.). Types of recurrence in simple dynamical systems (Russian), Akad. Nauk Ukrain. SSR, Inst. Mat. Preprint, 1991, no. 2, 16 pp. (with Fedorenko, V. V.).
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1980-1989 |
A method of difference equations in a resonator problem with a nonlinear reflector (Russian), Dokl. Akad. Nauk SSSR 309, 1989, no. 2, 327-331; translation in Soviet Phys. Dokl. 34, 1989, no. 11, 977-979 (1990) (with Lukin, K. A.; Maistrenko, Yu. L.; Shestopalov, V. P.). Characterizations of weakly chaotic maps of the interval, Proc. Amer. Math. Soc. 110, 1990, no. 1, 141-148 (with Fedorenko, V. V.; Smital, Ya.). Dynamics of difference equations (Ukrainian), U sviti matematyki [In the World of Mathematics] 19, Radianska shkola, Kyiv, 1989, 77-90 (with Ivanov, A. F.). How complicated can be one-dimensional dynamical systems: descriptive estimates of sets, Dynamical systems and ergodic theory (Warsaw, 1986), Banach Center Publ., 23, Warsaw, 1989, 447-453. Self-stochasticity in deterministic systems (Russian), Akad. Nauk Ukrain. SSR, Inst. Mat. Preprint 1989, no. 66, 15 pp. (with Romanenko, E. Yu.). Characterization of some classes of maps of an interval with zero topological entropy (Russian), Akad. Nauk Ukrain. SSR, Inst. Mat. Preprint 1989, no. 58, 18p. (with Smital, Ya.; Fedorenko, V. V.). A map with zero topological entropy that has a continuum of Cantor minimal sets (Russian), Dynamical systems and turbulence, Akad. Nauk Ukrain. SSR, Inst. Mat., Kyiv, 1989, 109-117. Classification of one-dimensional dynamical systems, European Conf. on Iteration Theory (ECIT-87, Caldes de Malavella, 1987), World Sci. Publ., 1989, 42-55. Oscillation of solutions of one class differential-difference equations (Russian), Proc. of Vekua Institute of Appl. Math., 3 (3), Tbilisi, 1988 (with Ivanov, A. F.). Attractors of difference equations and turbulence, Plasma theory and nonlinear and turbulent processes in physics (Kyiv, 1987), World Sci. Publ., Singapore, 1988, 520-536 (with Maistrenko, Yu. L.; Romanenko, E. Yu.). Strange attractors (Ukrainian), U sviti matematyki [In the World of Mathematics] 18, Radianska shkola, Kyiv, 1987, 61-80 (with Ivanov, A. F.). Difference equations with continuous time as mathematical models of the structure emergences, Dynamical systems and environmental models (Eisenach, 1986), Math. Ecol., Akademie-Verlag, Berlin, 1987, 40-49 (with Maistrenko, Yu. L.). Qualitative investigation of some boundary value problems: complex oscillation regimes (Russian), Functional-differential equations and their application to nonlinear boundary value problems, Akad. Nauk Ukrain. SSR, Inst. Mat., Kyiv, 1987, 74-87 (with Romanenko, E. Yu.). One-dimensional initial-boundary value problems of electrodynamics with nonlinear boundary conditions (Russian), Akad. Nauk Ukrain. SSR, Inst. Mat. Preprint 1987, no. 39, 28p. (with Lukin, K. A.; Maistrenko, Yu. L.; Shestopalov, V. P.). Asymptotic periodicity of solutions of difference equations with continuous time (Russian), Ukrain. Mat. Zh. 39, 1987, no. 1, 123-129 (with Maistrenko, Yu. L.; Romanenko, E. Yu.). Dry turbulence (Russian), Mathematical mechanisms of turbulence, Akad. Nauk Ukrain. SSR, Inst. Mat., Kyiv, 1986, 75-89 (with Maistrenko, Yu. L.; Romanenko, E. Yu.). Asymptotic properties of a semigroup of mappings of the interval (Russian), Dynamical systems and differential-difference equations, Akad. Nauk Ukrain. SSR, Inst. Mat., Kyiv, 1986, 75-89 (with Romanenko, E. Yu.). Qualitative investigation of some problems for the wave equation (Russian), Dynamical systems and differential-difference equations, Akad. Nauk Ukrain. SSR, Inst. Mat., Kyiv, 1986, 5-13 (with Aliev, S. Ya.). Boundary value problems for simple hyperbolic systems. Pattern formation and transition to chaos (Russian), Akad. Nauk Ukrain. SSR, Inst. Mat. Preprint 1985, no. 39, 31 p. (with Vereikina, M. B.; Maistrenko, V. L.; Romanenko, E. Yu.). Turbulence and simple hyperbolic systems, Mathematical analysis, Teubner-Texte Math. 79, Leipzig, 1985, 220-235 (with Maistrenko, Yu. L.). Dry turbulence (Russian), Proc. II Intern. Workshop "Nonlinear and Turbulent Processes" (Kyiv, 1985), 2, Naukova Dumka, 1985, 114-118. Descriptive estimates for the set of homoclinic points of a dynamical system (Russian), Differential-difference equations and problems of mathematical physics, Akad. Nauk Ukrain. SSR, Inst. Mat., Kyiv, 1984, 109-115. Oscillations of relaxation and turbulence type: differential-difference models (Russian), 9th Intern. Conf. on Nonlinear Oscillations (Kyiv, 1981), vol. 2, Naukova Dumka, Kyiv, 1984, 430-434. "Dry" turbulence, Nonlinear and turbulent processes in physics (Kyiv, 1983), vol. 3, Harwood Academic Publ., 1984, 1621-1626. Singular perturbations of difference equations with continuous time (Russian), Akad. Nauk Ukrain. SSR, Inst. Mat. Preprint 1984, no. 33, 40 pp. (with Aliev, S. Ya.; Ivanov, A. F.; Maistrenko, Yu. L.). Nonlinear boundary value problems for one-dimensional hyperbolic systems: asymptotically discontinuous solutions and their bifurcations (Russian), Dokl. Akad. Nauk Ukrain. SSR, Ser. A, 1984, no. 12, 27-30 (with Krasnyuk, I. B.; Maistrenko, Yu. L.). Development of the theory of differential equations at the Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR (Russian), Ukrain. Mat. Zh. 36, 1984, no. 5, 597-601 (with Shevelo, V. N.). Chaos in simple difference, differential-difference and partial differential equations (Russian), Sem. Inst. Prikl. Mat., Dokl. 18, Tbilisi, 1984, 18-26. The set of almost-recurrent points of a dynamical system (Russian), Dokl. Akad. Nauk Ukrain. SSR, Ser. A, 1984, no. 1, 6-9 (with Vereikina, M. B.). Turbulence and simple hyperbolic systems (Russian), Akad. Nauk Ukrain. SSR, Inst. Mat. Preprint 1984, no. 2, 23 p. (with Maistrenko, Yu. L.). Difference equations and dynamics of population size (Russian), Mathematical methods in biology (Katsiveli, 1979), Naukova Dumka, Kyiv, 1983, 143-156. Dry turbulence, Intern. Math. Congress (Warszawa), 1983, Short reports 10, p.12. Universal order and universal rate of bifurcations of solutions of differential-difference equations (Russian), Approximate and qualitative methods of the theory of functional differential equations, Akad. Nauk Ukrain. SSR, Inst. Mat., Kyiv, 1983, 98-106 (with Sivak, A. G.). Recurrence in one-dimensional dynamical systems (Russian), Approximate and qualitative methods of the theory of functional differential equations, Akad. Nauk Ukrain. SSR, Inst. Mat., Kyiv, 1983, 35-46 (with Vereikina, M. B.). C^∞-mappings of an interval with attracting cycles of arbitrarily large periods (Russian), Ukrain. Mat. Zh. 35, 1983, no. 4, 537-539 (with Ivanov, A. F.). On some results of qualitive investigation of differential-functional equations of first order (Russian), II Intern. Conf. "Func.-Diff. Syst. and Related Topics" (Zielona Gora, 1982), Poland (with Shevelo, V. N.; Ivanov, A. F.). Difference equations and the dynamics of the size of populations (Russian), Akad. Nauk Ukrain. SSR, Inst. Mat. Preprint 1982, no. 18, 22 p. On some properties of discrete dynamical systems, Iteration theory and its applications (Toulouse, 1982), Colloq. Internat. CNRS, 332, Paris, 1982, 153-158. Asymptotically periodic solutions of the differential-difference equations of neutral type, Proc. II Conf. "Differential Equations and Applications" (Ruse, 1981), Tech. Univ., Ruse, 1982 (with Maistrenko, Yu. L.; Romanenko, E. Yu.). Asymptotic behavior of solutions of differential-difference equations (Russian), Proc. II Conf. on Differential Equations and Applications (Ruse, 1981), Tech. Univ., Ruse, 1982, 835-846. Stability of a dynamical system's property of having a homoclinic trajectory (Russian), Oscillation and stability of solutions of functional-differential equations, Akad. Nauk Ukrain. SSR, Inst. Mat., Kyiv, 1982, 111-113 (with Fedorenko, V. V.). Asymptotic behavior of bounded solutions of systems of difference equations (Russian), Oscillation and stability of solutions of functional-differential equations, Akad. Nauk Ukrain. SSR, Inst. Mat., Kyiv, 1982, 75-86 (with Romanenko, E.Yu.; Slyusarchuk, L. M.). Periodic solutions of certain classes of differential-difference equations (Russian), Oscillation and stability of solutions of functional-differential equations, Akad. Nauk Ukrain. SSR, Inst. Mat., Kyiv, 1982, 25-34 (with Ivanov, A. F.). The asymptotic behavior of solutions of differential-difference equations (Russian), Qualitative methods for investigating nonlinear differential equations and nonlinear oscillations (Uzhgorod, 1980), Akad. Nauk Ukrain. SSR, Inst. Mat., Kyiv, 1981, 171-199 (with Romanenko, E. Yu.). The measure of repellers of one-dimensional smooth mappings (Russian), Functional-differential and difference equations, Akad. Nauk Ukrain. SSR, Inst. Mat., Kyiv, 1981, 16-22 (with Kolyada, S. F.). Asymptotically periodic solutions of a class of differential-difference equations (Russian), Dokl. Akad. Nauk Ukrain. SSR, Ser. A, 1981, no. 7, 27-31 (with Maistrenko, Yu. L.; Romanenko, E. Yu.). Integral-difference equations and dynamics of the size of populations (Russian), Differential equations and their application 29, Vilnius, 1981, 69-78 (with Maistrenko, Yu. L.; Romanenko, E. Yu.). Qualitative analysis of some types of differential-difference equations, Functional differential systems and related topics (Proc. First Intern. Conf., Blazejewko, 1979), Higher College Engrg., Zielona Gora, 1980, 334-340. Qualitative investigation of a class of differential-difference equations (Russian), Qualitative investigations of functional differential equations, Naukova Dumka, Kyiv, 1980, 129-144 (with Romanenko, E. Yu.). Continuous mappings of an interval with closed sets of periodic points (Russian), An investigation of differential and differential-difference equations, Akad. Nauk Ukrain. SSR, Inst. Mat., Kyiv, 1980, 137-145 (with Fedorenko, V. V.). Qualitative behavior of solutions of quasilinear differential-difference equations (Russian), An investigation of differential and differential-difference equations, Akad. Nauk Ukrain. SSR, Inst. Mat., Kyiv, 1980, 38-50 (with Maistrenko, Yu. L.; Romanenko, E. Yu.).
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1970-1979 |
Functional-differential equations that are close to functional equations (Russian), Asymptotic methods in the theory of nonlinear oscillations (Proc. All-Union Conf. Asymptotic Methods in Nonlinear Mechanics, Katsiveli, 1977), Naukova Dumka, Kyiv, 1979, 178-209 (with Romanenko, E. Yu.). Functional-differential equations with a finite group of argument transformations (Russian), Asymptotic behavior of solutions of functional-differential equations, Akad. Nauk Ukrain. SSR, Inst. Mat., Kyiv, 1978, 118-142. Asymptotic behavior of the solutions of linear functional-differential equations (Russian), Asymptotic behavior of solutions of functional-differential equations, Akad. Nauk Ukrain. SSR, Inst. Mat., Kyiv, 1978, 5-39 (with Romanenko, E. Yu.). On oscillations generated delay (Russian), Third National Congress on Theor. Appl. Mechanics, (Varna, 1977), Reports 1, Bulg. Acad. Sci, Sofia (with Shevelo, V. N.). Classical functional equations: fundamental concepts, methods and results (Russian), Differential equations with deviating argument (Proc. 4th All-Union Conf., Kyiv, 1975), Naukova Dumka, Kyiv, 1977, 290-297. Development of the theory of differential equations with deviating argument at the Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR (Russian), Differential equations with deviating argument (Proc. 4th All-Union Conf., Kyiv, 1975), Naukova Dumka, Kyiv, 1977, 215-221 (with Mitropolsky, Yu. A.). Linear difference equations with periodic coefficients (Russian), Qualitative methods in the theory of differential equations with deviating argument, Inst. Mat. Akad. Nauk Ukrain. SSR, Kyiv, 1977, 91-100 (with Pelyukh, G. P.). Lowering the number of transformations of the argument in functional and differential-functional equations (Russian), Qualitative methods in the theory of differential equations with deviating argument, Inst. Mat. Akad. Nauk Ukrain. SSR, Kyiv, 1977, 57-70 (with Maistrenko, Yu. L.). Structural theory of differentiable dynamical systems and weakly nonwandering points (Russian), VII Intern. Konferenz uber Nichtlineare Schwingungen (Berlin, 1975), Akademie-Verlag,Berlin, 1977, 193-200. Oscillatory nature and asymptotic behavior of the solutions of a class of differential equations with deviating argument (Russian), Problems of the asymptotic theory of nonlinear oscillations, Naukova Dumka, Kyiv, 1977, 257-263 (with Shevelo, V. N.). The state and prospects of development of the theory of differential equations with deviating argument. Fourth All-Union Conference on the Theory and Applications of Differential Equations with Deviating Argument (Kyiv, 1975) (Russian), Ukrain. Mat. Zh. 28, 1976 no. 2, 279-282 (with Mitropolsky, Yu. A.; Romanenko, E. Yu.; Shevelo, V. N.). The Fourth All-Union Conference on the Theory and Applications of Differential Equations with Deviating Argument (Kyiv, September 23-26, 1975) (Russian), Uspehi Mat. Nauk 31, 1976, no. 3, 231-238 (with Mitropolsky, Yu. A.; Myshkis, A. D.). Functional and functional-differential equations in which the deviation of the argument depends on the unknown function (Russian), Functional and differential-difference equations, Inst. Mat. Akad. Nauk Ukrain. SSR, Kyiv, 1974, 148-155. The stability of the solutions of differential equations with retarded argument (Russian), Functional and differential-difference equations, Inst. Mat. Akad. Nauk Ukrain. SSR, Kyiv, 1974, 141-147 (with Khusainov, D. Ya.). General solution of a system of functional equations in the neighborhood of a singular point (Russian), Functional and differential-difference equations, Inst. Mat. Akad. Nauk Ukrain. SSR, Kyiv, 1974, 100-109 (with Pelyukh, G. P.). Globally stable dynamical systems (Russian), Proc. Sixth Intern. Conf. Nonlinear Oscillations, Poznan, 1972, Part II, Polish Sci. Publ., Warsaw, 1974, 61-66. General solution of a certain class of nonlinear differential-functional equations of neutral type (Russian), Methods of approximate solution of differential and integral equations, Inst. Mat. Akad. Nauk Ukrain. SSR, Kyiv, 1973, 208-229 (with Pelyukh, G. P.). Nonwandering points of dynamical systems (Russian), Dynamical systems and questions on the stability of the solutions of differential equations, Inst. Mat. Akad. Nauk Ukrain. SSR, Kyiv, 1973, 165-174 (with Dobrynsky, V. A.). The stability of motion with respect to part of the variables (Russian), Dynamical systems and questions on the stability of the solutions of differential equations, Inst. Mat. Akad. Nauk Ukrain. SSR, Kyiv, 1973, 122-127 (with Khusainov, D. Ya.). Reconstructibility of expanding endomorphisms from the system of omega-limit sets (Russian), Dynamical systems and questions on the stability of the solutions of differential equations, Inst. Mat. Akad. Nauk Ukrain. SSR, Kyiv, 1973, 28-34 (with Bondarchuk, V. S.). The partially ordered system of omega-limit sets of expanding endomorphisms (Russian), Dynamical systems and questions on the stability of the solutions of differential equations, Inst. Mat. Akad. Nauk Ukrain. SSR, Kyiv, 1973, 128-164 (with Bondarchuk, V. S.). Orbit stability of trajectories (Russian), Differentsialnye Uravneniya 9, 1973, no. 3, 558-559 (with Dobrynsky,V.A.). Characterization of the cosine (Russian), Aequationes Mathematical 9, 1973, no. 3, 121-128. Genericity of the dynamical systems almost all of whose trajectories are stable under constantly acting perturbations (Russian), Dokl. Akad. Nauk SSSR 211, 1973, no. 2, 273-276 (with Dobrynsky, V. A.). Representation of the solutions of linear differential-difference equations of neutral type (Russian), Differentsialnye Uravneniya 9, 1973, no. 9, 1627-1645 (with Polishchuk, V. M.). The solutions of an overdetermined system of functional equations (Russian), The method of integral manifolds in nonlinear differential equations, Inst. Mat. Akad. Nauk Ukrain. SSR, Kyiv, 1973, 220-232 (with Romanenko, E. Yu.). Stability in the large of trajectories and dynamical systems (Russian), Ninth mathematical summer school (Katsiveli, 1971), Inst. Mat. Akad. Nauk Ukrain. SSR, Kyiv, 1972, 349-360. Set of orbit-stable trajectories of a dynamical system (Russian), Asymptotic and qualitative methods in the theory of nonlinear oscillations, Inst. Mat. Akad. Nauk Ukrain. SSR, Kyiv, 1971, 204-207. General solution of linear differential-difference equations of neutral type (Russian), Differential-difference equations, Inst. Mat. Akad. Nauk Ukrain. SSR, Kyiv, 1971, 125-139 (with Polishchuk, V. M.). Behavior of a Mapping in the Neighborhood of a Atrracting Set, Amer. Math. Soc. Transl. 97, 1970, no. 2, 227-258. A Classification of Fixed Points, Amer. Math. Soc. Transl. 97, 1970, no. 2, 159-179. A characterization of elementary and special functions by means of functional relations (Ukrainian), Dopovidi Akad. Nauk Ukrain. RSR, Ser. A, 1970, no. 11, 994-998 (with Pelyukh, G. P.). Problem of the uniqueness of the solutions of differential equations with deviating argument (Russian), Mathematical Physics, no. 8 , Naukova Dumka, Kyiv, 1970, 167-172. Existence and uniqueness of the solutions of a certain class of functional equations (Ukrainian), Dopovidi Akad. Nauk Ukrain. RSR, Ser. A, 1970, no. 9, 790-793 (with Pelyukh, G. P.).
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1960-1969 |
About isomorphism problem of dynamical systems (Russian), Proc. Intern. Conf. on Nonlinear Oscillations (Kyiv, 1969), vol. 2: Qualitative methods in the theory of nonlinear oscillations, Inst. Mat. Akad. Nauk Ukrain. SSR, Kyiv, 1970, 541-545. Orbital stability (Russian), Proc. Intern. Conf. on Nonlinear Oscillations (Kyiv, 1969), vol. 2: Qualitative methods in the theory of nonlinear oscillations, Inst. Mat. Akad. Nauk Ukrain. SSR, Kyiv, 1970, 209-215 (with Kasperov, V. N.). Smooth solutions of functional and differential-difference equations (Russian), Proc. Intern. Conf. on Nonlinear Oscillations (Kyiv, 1969), vol. 1: Analitic methods in the theory of nonlinear oscillations, Inst. Mat. Akad. Nauk Ukrain. SSR, Kyiv, 1970, 598-602. Realizable dynamical systems on two-dimensional manifolds (Russian), Trudy Sem. Mat. Fiz. 3, Kyiv, 1969, 330-336 (with Khusainov, D. Ya.). Rough dynamical systems (Ukrainian), IV conf. of young mathematicians of Ukraine (Kyiv, 1968), Inst. Mat. Akad. Nauk Ukrain. SSR, Kyiv, 1968, 146-150. Uniqueness conditions for functional equations (Russian), Trudy Sem. Mat. Fiz. Nelinein. Koleban. 1, Naukova Dumka, Kyiv, 1968, no. 2, 262-268. The set of attraction of periodic points (Russian), Trudy Sem. Mat. Fiz. Nelinein. Koleban. 1, Naukova Dumka, Kyiv, 1968, no. 2, 126-129 (with Kasperov, V. N.). The center of a structurally stable dynamical system (Russian), Ukrain. Mat. Zh. 20, 1968, no. 5, 717-719. Attracting sets containing no cycles (Russian), Ukrain. Mat. Zh. 20, 1968, no. 1, 136-142. On the periodic solutions of a class of finite difference equations, Proceed. IV conf. on nonlinear oscillations (Prague, Sept. 5-9, 1967), Academia, Prague, 1968, p. 249. On a theorem of G. D. Birkhoff (Ukrainian), Dopovidi Akad. Nauk Ukrain. RSR, Ser. A, 1967, no. 5, 429-432. Endomorphism properties on omega-limit sets (Russian), Intern. Math. Congress (Moscow,1966), Short reports. Continuous mapping on the set of limit points of an iteration sequence (Russian), Ukrain. Mat. Zh. 18, 1966, no. 5, 127-130. Partially ordered system of attracting sets (Russian), Dokl. Akad. Nauk SSSR 170, 1966, no. 6, 1276-1278; (English) Soviet Math. Dokl. 7, no. 5, 1966, 1384-1386. Behavior of a map in the neighborhood of an attracting set (Russian), Ukrain. Mat. Zh. 18, 1966, no. 2, 60-83. On convergence set for one-dimensional iterations (Ukrainian), Dopovidi Akad. Nauk Ukrain. RSR 7, 1966, 866-870. A classification of fixed points (Russian), Ukrain. Mat. Zh. 17, 1965, no. 5, 80-95. On attracting and attracted sets (Russian), Dokl. Akad. Nauk SSSR 160, 1965, no. 5, 1036-1038; (English) Soviet Math. Dokl. 6, 1965, 268-270. Continuous mapping on a set of omega-limit points (Ukrainian), Dopovidi Akad. Nauk Ukrain. RSR 11, 1965, 1407-1410. On properties of the set of limit points of an iterative sequence of a continuous function (Russian), Volzh. Mat. Sb. 3, 1965, 343-348 (with Kenzhegulov, H. K.). On cycles and the structure of a continuous mapping (Russian), Ukrain. Mat. Zh. 17, 1965, no. 3, 104-111. Fixed points and the center of a continuous mapping of the line into itself (Ukrainian), Dopovidi Akad. Nauk Ukrain. RSR 7, 1964, 865-868. Coexistence of cycles of a continuous mapping of the line into itself (Russian), Ukrain. Mat. Zh. 16, 1964, no. 1, 61-71. The reducibility of a continuous function of a real variable and the structure of the fix points of the corresponding iteration process (Russian), Dokl. Akad. Nauk SSSR 139, 1961 no. 5, 1067-1070; (English) Soviet Math. Dokl. 2, 1961. Solutions of a class of functional equations (Russian), Ukrain. Mat. Zh. 13, 1961, no. 3, 86-94. Rapidly converging iterative processes (Russian), Ukrain. Mat. Zh. 13, 1961, no. 2, 210-215. Necessary and sufficient conditions for convergence of one-dimensional iterative processes (Russian), Ukrain. Mat. Zh. 12, 1960, no. 4, 484-489.
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