Institute of Mathematics
National Academy of Sciences of Ukraine
Tereshchenkivs'ka 3, 01601, Kyiv
Ukraine
Room:
322
Phone:
+380-44-2343036
Homepage:
http://www.imath.kiev.ua/~skolyada/
Course of Lectures:
Topological Dynamics: Minimality, Entropy and Chaos
Main aim:
The study of topological transitivity, minimality,
chaotic properties, topological entropy and functional envelopes for
discrete dynamical systems given by compact Hausdorff (metric)
spaces and continuous selfmaps.
Contents:
Topological transitivity and minimality
Li-Yorke sensitivity and other concepts of chaos
Topological entropy
Functional envelope of a dynamical systemy
Prerequisites:
Basic knowledge Functional Analysis and Topology.
Lecture Time:
Tuesdays, 14:30 - 16:00
Exercise Time:
Thursdays, 15:00 - 16:00
First class:
13 January 2015
Room:
305, 208 or 322
Detailed List of Contents of the Lectures:
Topological Dynamics: Minimality, Entropy and Chaos
1. Topological transitivity and minimality:
Lecture 1 - Topologically transitive maps
Lecture 2 - Minimal maps and minimal spaces
Lecture 3 - Minimal sets on manifolds
2. Li-Yorke sensitivity and other concepts of chaos:
Lecture 4 - Chaotic interval maps
Lecture 5 - Topological chaos and Li-Yorke chaos
Lecture 6 - Li-Yorke sensitivity
Lecture 7 - Topologically weakly mixing systems
Lecture 8 - On Lyapunov numbers
3. Topological entropy:
Lecture 9 - Topological entropy of a (nonautonomous) dynamical system
Lecture 10 - Topological entropy of (nonautonomous) piecewise-monotone
dynamical systems on the interval
Lecture 11 - Group homeomorphisms and topological entropy of their elements
4. Functional envelope of a dynamical system:
Lecture 12 - Topological transitivity of a functional envelope
Lecture 13 - Topological entropy of a functional envelope
