Entropy of polyhedral billiard

TL;DR

This paper proves that the billiard map in a convex polyhedron in three-dimensional space has zero topological entropy, indicating predictable and non-chaotic dynamics.

Contribution

The work establishes the zero topological entropy property for billiard maps in convex polyhedra, a significant step in understanding their dynamical complexity.

Findings

Billiard map in convex polyhedra has zero topological entropy.

The result implies non-chaotic, predictable dynamics in such systems.

Advances understanding of billiard dynamics in higher dimensions.

Abstract

We consider the billiard map in a convex polyhedron of $\mathbb{R}^3$, and we prove that it is of zero topological entropy.