Lower bounds for the number of closed billiard trajectories of period 2 and 3 in manifolds embedded in Euclidean space

TL;DR

This paper establishes a lower bound on the minimum number of closed billiard trajectories with periods 2 and 3 in manifolds embedded in Euclidean space, advancing understanding of billiard dynamics in geometric manifolds.

Contribution

It provides the first known lower bounds for the count of 2- and 3-periodic billiard trajectories in such manifolds.

Findings

Lower bounds for 3-periodic billiard trajectories in embedded manifolds.

Insights into the minimal number of closed billiard paths of specific periods.

Advancement in geometric billiard trajectory theory.

Abstract

A lower bound for the number of 3-periodical billiard trajectories in a manifold embedded in Euclidean space is obtained.