Statistical properties of type D dispersing billiards

TL;DR

This paper studies type D dispersing billiards with unbounded free flight, proving exponential decay of correlation and other statistical properties for a class of such systems.

Contribution

It establishes exponential decay of correlation and related statistical properties for a specific class of non-degenerate type D dispersing billiards.

Findings

Proves exponential decay of correlation.

Demonstrates statistical properties for type D billiards.

Analyzes billiards with unbounded free flight functions.

Abstract

We consider dispersing billiard tables whose boundary is piecewise smooth and the free flight function is unbounded. We also assume there are no cusps. Such billiard tables are called type D in the monograph of Chernov and Markarian. For a class of non-degenerate type D dispersing billiards, we prove exponential decay of correlation and several other statistical properties.