Approximation and billiards

Serge Troubetzkoy (1, 2, 3, 4)

1 IML - Institut de mathématiques de Luminy
2 CPT - Centre de Physique Théorique - UMR 6207
3 FRUMAM - Fédération de Recherche des Unités de MAthématiques de Marseille
4 CPT - Centre de Physique Théorique - UMR 7332

This survey is based on a series of talks I gave at the conference ``Dynamical systems and diophantine approximation'' at l'Instut 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.

Domaines: Systèmes dynamiques [math.DS]

Serge Troubetzkoy. Approximation and billiards. Dynamical systems and Diophantine approximation, 2009, Paris, France. pp.173-185. ⟨hal-00115001v2⟩