# Topologically weakly mixing polygonal billiards

## TL;DR

This paper proves that in most polygons, the billiard dynamics and the associated symbolic coding exhibit topological weak mixing, indicating complex and unpredictable orbit behavior.

## Contribution

It establishes that topological weak mixing is typical in polygonal billiards, advancing understanding of their dynamical complexity.

## Key findings

- Billiard maps in typical polygons are topologically weakly mixing.
- Associated symbolic subshifts also exhibit topological weak mixing.
- Results suggest high unpredictability in polygonal billiard dynamics.

## Abstract

We show that in a typical polygon the billiard map as well as its associated subshift obtained by coding orbits by the sequence of sides they visit are topologically weakly mixing.