Approximation and billiards

Details Approximation and billiards Approximation and billiards

2006-11-20

arxiv.org/abs/math/0611599v2

Mathematics

Dynamical Systems

Scientific paper

This survey is based on a series of talks I gave at the conference ``Dynamical systems and diophantine approximation'' at l'Instut Henri Poincar\'e in June 2003. I will present asymptotic results (transitivity, ergodicity, weak-mixing) for billiards based on the approximation technique developed by Katok and Zemlyakov. I will also present approximation techniques which allow to prove the abundance of periodic trajectories in certain irrational polygons.

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