Markov partitions for billiards
Ergodic Theory and Dynamical Systems Seminar
21st February 2019, 2:00 pm – 3:00 pm
Howard House, 4th Floor Seminar Room
Symbolic dynamics is a tool that simplifies the study of dynamical systems in various aspects. One approach to obtain symbolic dynamics is constructing Markov partitions: if properly constructed, then the system has properties similar to Markov chains in probability. In this talk, we will discuss the recent developments of this approach for non-uniformly hyperbolic
planar billiards. A consequence is a new estimate on the number of periodic trajectories for the billiard map of some Sinai billiards.