C^1-generic billiard tables have a dense set of periodic points

TL;DR

This paper proves that in a typical C^1-billiard table, the set of periodic points is densely distributed throughout the phase space, highlighting a fundamental property of billiard dynamics.

Contribution

It establishes that for a generic class of C^1-billiard tables, the periodic points form a dense subset in the phase space, a new result in billiard dynamics.

Findings

Periodic points are dense in the phase space for generic C^1-billiard tables.

The result applies to a broad class of billiard tables with C^1 regularity.

This advances understanding of the structure of billiard dynamical systems.

Abstract

We prove that the set of periodic points of a generic C^1-billiard table is dense in the phase space.