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Ergodic properties of rational billiards

Francisco Andres Arana Herrera, U. of Maryland
Wednesday, May 22, 2024 - 4:30pm to 5:30pm
PDL C-38

The ergodic properties of rational billiards, i.e., billiards on a table whose angles are rational multiples of pi, have been a subject of intense study in dynamical systems. A famous result of Kerckhoff, Masur, and Smillie shows that rational billiards are uniquely ergodic in almost every direction. A famous result of Katok shows that rational billiards are not mixing in any direction. What about the intermediate regime of weak mixing, i.e., mixing modulo a negligible set of exceptions? In this talk we show that rational billiards are weak mixing in almost every direction unless a natural algebraic/geometric obstruction is present. Furthermore, this obstruction vanishes in 'most' cases. This is joint work in progress with Jon Chaika and Giovanni Forni.

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