Persistence of periodic billiard orbits under domain deformation

TL;DR

This paper proves that certain periodic billiard orbits persist under continuous deformation of polygonal domains, maintaining their combinatorial type across a family of polygons.

Contribution

It establishes the persistence of specific periodic billiard orbits under domain deformation, extending understanding of billiard dynamics in polygonal shapes.

Findings

Periodic billiard orbits persist under domain deformation.

Persistence holds for polygons satisfying a combinatorial criterion.

Every polygon in the deformation path admits a similar periodic orbit.

Abstract

We prove that if a polygon admits a periodic billiard orbit satisfying a certain combinatorial criterion, then there are paths of polygons in parameter space for which every polygon in the path admits a periodic billiard orbit of the same type.