Lecture 5. Vadim Kaloshin: «Markov partitions and coding the cat map»
Channel: Projekt MmF
Date: 2023-08-15

One of the most illuminating examples of chaotic dynamical systems is Arnold's cat map. It was introduced by Vladimir Arnold about 60 years ago.  In this lecture, we will see how to use so-called Markov partitions to encode the orbits of the cat map, to find an exact formula for the number of periodic orbits of a given period, and to compute the entropy of the cat map, which is a measure of its chaos. These techniques turn out to apply to a large class of what is called hyperbolic systems. 

Speaker

Vadim Kaloshin is a professor at the Institute of Science and Technology Austria. He has made spectacular contributions in the fields of dynamical systems and celestial mechanics. Recently, he has settled the so-called local version of conjecture due to George Birkhoff on the shape of integrable, strictly convex billiard tables. This conjecture had stood for almost a century! Vadim was born and raised in Kharkiv, where he attended Kharkiv Physics and Mathematics Lyceum No. 27.