13 Feb 2001

Boris Kruglikov "Positive topological entropy of integrable systems: Entropy".

The purpose of this series of lectures is to consider on examples some interesting phenomena in the theory of dynamical systems. It was believed that positivity of entropy serves as a criterion for chaos. Recent examples by Bolsinov and Taimanov extended by the author to the non-holonomic case show this contradicts another belief that integrable systems are not chaotic. This seeming contradiction is due to: 1) absence of mathematical definition of the chaos, 2) lack of specification of type of entropy, kind of integrability etc. We discuss existing and possible relations.

On the first lecture the definition and various properties of the entropy of discrete and continuous time dynamical systems will be discussed. No special knowledge is assumed.