An upper bound on topological entropy of the Bunimovich stadium billiard map

TL;DR

This paper establishes an upper bound on the topological entropy of the billiard map in a Bunimovich stadium, providing insight into the system's complexity.

Contribution

It introduces a new upper bound for the topological entropy specific to the Bunimovich stadium billiard map.

Findings

Topological entropy of the billiard map is at most log(3.49066)

Provides a quantitative measure of complexity for the Bunimovich stadium

Advances understanding of dynamical properties of billiard systems

Abstract

We show that the topological entropy of the billiard map in a Bunimovich stadium is at most log(3.49066).