On the lower bounds for the number of periodic billiard trajectories in manifolds embedded in Euclidean space

TL;DR

This paper establishes a Morse-theoretic framework to estimate the minimum number of periodic billiard trajectories on manifolds embedded in Euclidean space, advancing understanding of billiard dynamics.

Contribution

It introduces a Morse theory approach specifically for periodic billiard trajectories, providing new lower bounds for their number on embedded manifolds.

Findings

Morse theory applied to billiard trajectories

New lower bounds for periodic billiard trajectories

Theoretical framework for billiard dynamics

Abstract

In this paper the problem of estimating the number of periodical billiard trajectories is considered. The main result is the theorem on Morse theory for periodical billiard trajectories.