Institut de Mathématiques de Luminy

Abstract 2006-24

Troubetzkoy Serge.
Approximation and billiards.

This survey is based on a series of talks I gave at the conference "Dynamical systems and diophantine approximation" at l’Institut Henri Poincaré 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.


Last update : december 4, 2006, EL.