Entropy and Complexity of Polygonal Billiards with Spy Mirrors

TL;DR

This paper investigates the complexity and entropy of polygonal billiards with spy mirrors, establishing that such systems have zero topological entropy and providing bounds on their complexity growth.

Contribution

It proves that polygonal billiards with spy mirrors have zero topological entropy and offers bounds on their complexity growth rates.

Findings

Zero topological entropy for billiards with spy mirrors

Sub-exponential complexity in certain cases

Polynomial complexity estimates in other cases

Abstract

We prove that a polygonal billiard with one-sided mirrors has zero topological entropy. In certain cases we show sub exponential and for other polynomial estimates on the complexity.