### 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.

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