S e l e c t e d   P u b l i c a t i o n s  of  D e p a r t m e n t  of

 DYNAMICAL   SYSTEMS  THEORY

Books
  1. Difference Equation and Their Applications , A.N.Sharkovsky, Yu.L.Maistrenko, E.Yu.Romanenko Mathematics and its Applications,250, Kluwer Academic Publ., Dorbrecht, 1993, 358pp.(English translation with complements)
  2. Dynamics of one-dimensional maps, A.N. Sharkovsky, S.F. Kolyada, A.G. Sivak and V.V. Fedorenko Mathematics and its Applications,407, Kluwer Academic Publishers, Dorbrecht, 1997, 272pp. (English translation with complements)

Articles in journals/contributions to books                                                  since 1990
    1990
     
  1. V.V. Fedorenko, A.N. Sharkovsky and J. Smital, Characterizations of weakly chaotic maps of the interval, Proc. Amer. Math. Soc., 110, 1990, 141-148
  2. E.Yu,  Romanenko, Representation of the local general solution of a certain class of differential-functional equations. (English. Russian original) Ukrain. Math. J. 42, No.2, 182-186 (1990); translation from Ukrain. Mat. Zh. 42, No.2, 206-210 (1990)


    3. 1991
     

  3. V.V. Fedorenko and J. Smital, Maps of the interval Ljapunov stable on the set of nonwandering points, Acta Math. Univ. Comenianae, LX, 1991, 11-14
  4. S.F. Kolyada and A.N. Sharkovsky, On topological dynamics of triangular maps of the plane, Iteration Theory, Proc. ECIT-89. World Scientific Publishing, Singapore, 1991, 177-183


    5. 1992
     

  5.  A.F. Ivanov and  A.N.  Sharkovsky, Oscillations in singularly perturbed delay equations. 

    6. Dyn. Rep., Expo. Dyn. Syst., New Ser. 1, 1992, 164-224 
  6. S. F. Kolyada, On dynamics of triangular maps of the square, Ergodic Theory & Dynamical Systems, 12, 1992, 749-768
  7. S. Kolyada and L. Snoha, On omega-limit sets of triangular maps, Real Analysis Exchange, 18 , 1, 1992-93, 115-130
  8.  A.N. Sharkovsky and E.Yu. Romanenko, Ideal turbulence: Attractors of deterministic systems may lie in the space of random fields, Int. J. Bifurcation & Chaos, 2, No.1, 1992, 31-36 
  9. A.N. Sharkovsky and E.Yu.  Romanenko,  Problems of turbulence theory and iteration theory,  Iteration Theory, Proc. ECIT-91, World Scientific Publishing, Singapore, 1992,  242-252
  10. A.N. Sharkovsky and E.Yu. Romanenko, Self-stochasticity: attractors of deterministic problems may contain random functions, Dopovidi Ukrain. Akad. Nauk, 10, 1992, 33-37 (in Ukrainian)


    11. 1993
     

  11. Ll. Alseda and V.V. Fedorenko, Simple and complex dynamics for circle maps, Publ. Matematiqes, 37, 1993, 305-316
  12. Ll. Alseda, S.F. Kolyada and L. Snoha,  On topological entropy of triangular maps of the square. Bull. Aust. Math. Soc. 48,  1993, 55-67
  13. E.Yu. Romanenko and M.B. Vereikina, On simplest mathematical patterns and computer graphics, Ukrain. Math. J.,  45 (10), 1993, 1569--1582
  14. A.N. Sharkovsky, Chaos from a time-delayed Chua's circuit, EEE Trans. Circuits Syst., I, Fundam. Theory Appl. 40, No.10, 1993, 781-783 
  15. A.N. Sharkovsky and L.O. Chua, Chaos in some 1-D discontinuous maps that appear in the analysis of electrical circuits, IEEE Trans. Circuits Syst., I, Fundam. Theory Appl. 40, No.10, 1993, 722-731
  16. A.N. Sharkovsky, Yu.L.Maistrenko, Ph. Deregel and L.O. Chua, Dry  turbulence from a time-delay Chua's circuit, World scientific on Nonlinear Science, Ser. B, 1, 1993, 1018-1041
  17. Eh.E. Vajsleb and V.V. Fedorenko,  Representations of relation operators and one-dimensional dynamical systems.  Sel. Math. 12, 1993, 105-112 


    18. 1994
     

  18. A.N.Sharkovsky,  Ideal Turbulence in an idealized time-delayed Chua's circuit,  Internat. J. Bifurcation & Chaos, 4, No 2. 1994, 303-309
  19. A.N. Sharkovsky and  A.G. Sivak,  Universal phenomena in solution  bifurcations of some boundary value problems,  J. Nonlinear  Mathematical Physics, 1, 1994, 147-157
  20. A.G. Sivak, On the structure of minimal attraction centers of recurrent trajectories of continuous maps of the interval. Acta Math. Univ. Comen., New Ser. 63, 1994, 227-239


    21. 1995
     

  21. V.V. Fedorenko, Simple and complex dynamics for one-dimensional manifold maps, Intern. J. of Bifurcation & Chaos, 5, 1995, 1351-1355
  22.  E. Romanenko, On chaos in continuous difference equations, Dynamical systems and applications,  Agarwal, R. P. (ed.),Singapore: World Scientific. World Sci. Ser. Appl. Anal. 4, 1995, 617-630
  23. E.Yu. Romanenko,  A.N. Sharkovsky and M.B. Vereikina, Self-structuring and self-similarity in boundary value problems, Int. J. Bifurcation & Chaos, 5,  1995, 1407-1418 
  24. E.Yu. Romanenko and  A.N. Sharkovsky,  Self-Stochasticity in Dynamical Systems as a Scenario for Deterministic Spatio-Temporal  Chaos,  Chaos and Nonlinear Mechanics. Ser.B., 4, 1995, 172-181
  25. A.N. Sharkovsky, Universal phenomena in some infinite-dimensional dynamical systems. 

    26. Int. J. Bifurcation & Chaos, 5, 1995, 1419-1425
  26. A.N. Sharkovsky, Ph. Deregel and L.O. Chua, Dry turbulence and period-adding phenomena from a 1-D map with time delay. Int. J. Bifurcation & Chaos,  5, 1995, 1283-1302
  27.  A.G.  Sivak, The structure of minimal attraction centers of trajectories of continuous maps of the interval. Real Analysis Exchange , 20,  1995, 125-133.
  28. A.G.  Sivak,  An application of one-dimensional universality results to a class of difference-differential equations,  Proceedings of the first international conference on difference equations, Elaydi, Saber N. (ed.) et al.,Trinity University, San Antonio, TX, USA, May 25-28, 1994. London: Gordon and Breach. 1995, 483-494 


    29. 1996
     

  29. S. Kolyada and L. Snoha, Topological entropy of nonautonomous dynamical systems, Random & Computational Dynamics, 4, 2 & 3, 1996, 205-233
  30.  S. Kolyada and L. Snoha, Topological dynamics of triangular maps of the square, 

    31.  Iteration theory. Proc. ECIT92, Singapore: World Scientific. 1996, 165-171
  31. E.Yu. Romanenko and A.N. Sharkovsky,  From one-dimensional to infinite-dimensional dynamical systems: ideal turbulence,  Ukrain. Math. J., 48 (12), 1996, 1604-1627 (in Ukrainian), Ukrain. Math. J., 48 (12), 1996, 1817-1842
  32. O.M. Sharkovs'kij, A.F. Ivanov,  V.V. Fedorenko and O.D. Fedorenko, Coexistence of periodic orbits for a class of discontinuous maps. (Ukrainian) Dopov. Akad. Nauk Ukr. 1996, No.11, 21-25 
  33. A.G. Sivak, Each nowhere dense nonvoid closed set in $R^ n$ is a $\sigma$-limit set, Fundamenta Mathematicae , 149,  1996, 183-190


    34. 1997
     

  34. M.A.Aziz-Alaoui, R.Lozi, A.D, Fedorenko and A.N. Sharkovsky, Recovering trajectories of chaotic piecewise linear dynamical systems, Proceedings of the first international Conference "Control of Oscillations and Chaos", St.Petersburg, 2 , 1997, 230-233.
  35. S. Kolyada and L. Snoha, Some aspects of topological transitivity - a survey, Proc. ECIT-94, Grazer Math. Ber., 334, 1997, 3-35 
  36.  A.G. Sivak, On the periodicity of recursive sequences, Advances in difference equations. Proceedings of the 2nd international conference on difference equations, Veszprem, Hungary, August 7--11, 1995. Langhorne, PA: Gordon and Breach Science Publishers. 1997, 559-566
  37. M.B.Vereikina and  A.N.Sharkovsky, Shadowing property of dynamical systems

    38. and stubility of orbit prolongations, Ukrain. Math. J, 49,  1997, 1016-1024.

    1998
     

  38. A.D. Fedorenko, V.V. Fedorenko, A.F. Ivanov and A.N. Sharkovsky, Solution behaviour in a class of difference-differential equations, Bull. Austral. Math. Soc., 57, 1998, 37-48
  39. E.Yu. Romanenko,  On certain features of the long-time behavior of solutions for difference equations with continuous time and differential-difference equations of neutral type, in  Boundary value problems for differential equations, Inst. Mat., Ukrain.  Akad. Nauk, Kiev), 1 (17), 1998,  207-213 (in Russian)
  40. E.Yu.Romanenko, M.B.Vereikina and  A.N.Sharkovsky, Structural Turbulence in boudary value problems, Proceedings of the first international Conference "Control of Oscillations and Chaos", St.Petersburg, 3 , 492-497


    41. 1999
     

  41. Ll. Aseda, S. Kolyada, J. Llibre and L. Snoha, Entropy and periodic points for transitive maps ,  Trans. Amer. Math. Soc.,  351 (1999), 1551-1573
  42. S. Kolyada, M. Misiurewicz and L. Snoha, Topological entropy of nonautonomous piecewise monotone dynamical systems on the interval, Fundamenta Mathematicae , 160 (1999), 161--181
  43.  Yu.S. Mishura and Yu.V. Tomilov,  Method of successive approximations for abstract Volterra equations in a Banach space. (Ukrainian) Ukrain. Mat. Zh. 51, No.3, 1999, 376-382 
  44. E.Yu. Romanenko, M.B. Vereikina and  A.N. Sharkovsky, Self-stochasticity in deterministic boundary value problems, in Nonlinear Boundary Value Problems, 9, Inst. Appl. Math.and Mech.,

    45. NAN of Ukraine, Donetsk, 1999, 174-184
  45. E.Yu. Romanenko, M.B. Vereikina and A.N. Sharkovsky, Self-Structuring and Self-Stochasticity in Difference Equations and Some Boundary Value Problems, in "Self-Similar Systems", Proc. Intern. Conf. (Dubna, Russia), 1999, 237-250
  46. E.Yu. Romanenko and A.N. Sharkovsky, Dynamics of solutions for simplest nonlinear boundary value problems, Ukrain. Math. Zh., 51, no.6, 1999, 810-826  (in Ukrainian)
  47. E.Yu. Romanenko and  A.N. Sharkovsky, From boundary value problems to difference equations: A method of investigation of chaotic vibrations, Intern. J. Bifurcation & Chaos, 9, no.7, 1999, 1285-1306
  48. E.Yu. Romanenko and A.N. Sharkovsky, Long-time properties of solutions for one class of boundary value problems, Dopovidi Ukrain. Acad. Nauk, no.3, 1999, 43-48 (in Ukrainian)
  49. A.N. Sharkovsky and  S.A. Berezovsky, Computer Turbulence, in "Self-Similar Systems", Proc. Intern. Conf. (Dubna, Russia), 1999, 251-259
  50. A.N. Sharkovsky, Iteration of continuous functions and dynamics of solutions for 

    51. some boundary value problems, Ann. Math. Sil., 13, 1999, 243-255

Preprints (it includes some abstracts and downloadable PDF and PostScript files)
  1. S. Kolyada, L. Snoha and S. Trofimchuk, Noninvertible minimal maps, Preprint IML # 99-26 , Institut de Mathématiques de Luminy, Marseille, 18 pp., 1999 : abstract , PS file, PDF file 

    2.  

       Updated:   December 9, 1999