Limit Sets of Convex non Elastic Billiards

TL;DR

This paper introduces a class of convex non-elastic billiard systems with modified reflection laws that exhibit limit sets characterized by dominated splitting, including dynamics akin to rational or irrational rotations.

Contribution

It presents the first examples of convex non-elastic billiards with limit sets showing dominated splitting and rotational dynamics, inspired by Pujals and Sambarino's work.

Findings

Billiards with modified reflection laws can have limit sets with dominated splitting.

The dynamics include both rational and irrational rotations.

These examples expand understanding of non-elastic billiard systems.

Abstract

Inspired by the work of Pujals and Sambarino on dominated splitting, we present billiards with a modified reflection law which constitute simple examples of dynamical systems with limit sets with dominated splitting and where the dynamics is a rational or irrational rotation.