On the multiplicity of non-iterated periodic billiard trajectories

TL;DR

This paper develops an iteration theory for periodic billiard trajectories in convex domains and uses it to prove the existence of multiple distinct non-iterated trajectories.

Contribution

It introduces a novel iteration theory for billiard trajectories and establishes a new multiplicity result for non-iterated trajectories.

Findings

Established a multiplicity result for non-iterated billiard trajectories

Developed a new iteration theory for periodic billiard trajectories

Proved the existence of multiple distinct non-iterated trajectories

Abstract

We introduce the iteration theory for periodic billiard trajectories in a compact and convex domain of the Euclidean space, and we apply it to establish a multiplicity result for non-iterated trajectories.