a Billiard ? Yakov Sinai

Yakov G . Sinai , Abel Prize Laureate 2014

A dynamical billiard is an idealization of the game of billiard, but where the table can have shapes other than the rectangular and even be multidimensional. We use only one billiard ball, and the billiard may even have regions where the ball is kept out. Formally, a dynamical billiard is a dynamical system where a massless and point shaped particle moves inside a bounded region. The particle i...

A Theorem About Uniform Distribution

Ju n 20 02 Sinai billiards , Ruelle zeta - functions and Ruelle resonances : microwave experiments

We discuss the impact of recent developments in the theory of chaotic dynamical systems, particularly the results of Sinai and Ruelle, on microwave experiments designed to study quantum chaos. The properties of closed Sinai billiard microwave cavities are discussed in terms of universal predictions from random matrix theory, as well as periodic orbit contributions which manifest as ‘scars’ in e...

The Lyapunov exponent in the Sinai billiard in the small scatterer limit

We show that Lyapunov exponent for the Sinai billiard is λ = −2 log(R)+ C + O(R log R) with C = 1 − 4 log 2 + 27/(2π) · ζ(3) where R is the radius of the circular scatterer. We consider the disk-to-disk-map of the standard configuration where the disks is centered inside a unit square.

On Finding the Periodic Orbits of the Sinai Billiard