The billiard ball problem and rotation numbers

2009/02/24 by Eugene Gutkin, Gutkin, Eugene
Mathematics · #37A10 #37E45 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37A10 #msc:37E45

paper · pdf · doi:10.48550/arxiv.0902.4172

arxiv created 2009/02/24 · arxiv updated 2009/12/01

Abstract

We introduce the concepts of rotation numbers and rotation vectors for billiard maps. Our approach is based on the birkhoff ergodic theorem. We anticipate that it will be useful, in particular, for the purpose of establishing the non-ergodicity of billiard in certain domains.

Related

• Star-shaped trajectories of certain billiards around a triangle
• Devil's Staircase -- Rotation Number of Outer Billiard with Polygonal Invariant Curves
• Angular Billiard and Algebraic Birkhoff conjecture
• Dan Reznik's identities and more
• Computing Mather's β-function for Birkhoff billiards