Exponential Decay of Correlations for Finite Horizon Sinai Billiard Flows

TL;DR

This paper proves exponential decay of correlations for the Sinai billiard flow in a finite horizon Lorentz Gas, and analyzes the spectral properties of its transfer operator generator.

Contribution

It establishes exponential decay of correlations and characterizes the spectrum of the transfer operator for Sinai billiard flows with finite horizon.

Findings

Exponential decay of correlations proven for the flow.

Spectrum of the transfer operator characterized.

Resonances of the Sinai billiard flow analyzed.

Abstract

We prove exponential decay of correlations for the billiard flow associated with a two-dimensional finite horizon Lorentz Gas (i.e., the Sinai billiard flow with finite horizon). Along the way, we describe the spectrum of the generator of the corresponding semi-group L_t of transfer operators, i.e., the resonances of the Sinai billiard flow, on a suitable Banach space of anisotropic distributions. (Revised after referees' comments.)