Closed billiard trajectories with prescribed bounces

TL;DR

This paper analyzes the asymptotic growth rate of primitive periodic billiard trajectories in a 2D dispersive billiard, focusing on trajectories with a fixed number of bounces on one obstacle.

Contribution

It provides the first asymptotic estimates for the number of primitive periodic trajectories with prescribed bounce counts in dispersive billiards.

Findings

Asymptotic growth rate established for trajectories with fixed bounce counts.

Results apply to two-dimensional dispersive billiards.

Enhances understanding of billiard dynamics with constraints.

Abstract

We give the asymptotic growth of the number of primitive periodic trajectories of a two dimensional dispersive billiard, when we prescribe their number of bounces on one of the obstacles.