Bunimovich Stadium

mathematics

Published

November 14, 2020

The Bunimovich Stadium is one example of a Dynamical Billiards table that exhibits chaotic behavior even with only concave scatterings. Trajectories in the Bunimovich stadium exhibit (eventual) exponential divergence over time.

In addition, almost any trajectory in a Bunimovich stadium eventually gets arbitrarily close to any point of the stadium. This is in sharp contrast to trajectories in elliptical billiards: any one trajectory in elliptical billiards will always leave a chunk of the table unexplored.

Acknowledgments

Inspiration for this post came from Baez’s post on the stadium.

---
title: Bunimovich Stadium
categories: [mathematics]
date: 2020-11-14
image: /images/bunimovich-stadium.jpg
---

<script src="../src/lib/d3.v5.js"></script>

The Bunimovich Stadium is one example of a
[Dynamical Billiards](https://en.wikipedia.org/wiki/Dynamical_billiards)
table that exhibits chaotic behavior even with only concave
scatterings. Trajectories in the Bunimovich stadium exhibit (eventual)
exponential divergence over time.

In addition,
[almost any](https://en.wikipedia.org/wiki/Almost_surely) trajectory
in a Bunimovich stadium eventually gets arbitrarily close to any point of the
stadium. This is in sharp contrast to trajectories in elliptical
billiards: any one trajectory in elliptical billiards will always leave
a chunk of the table unexplored. 

<div id="main"></div>

<div id="reset-bunimovich"></div>
<div id="reset-elliptical"></div>
<div id="clear-tracks"></div>

<script type="module" src="bunimovich-stadium/main.js"></script>

## Acknowledgments

Inspiration for this post came from
[Baez's post on the stadium](http://blogs.ams.org/visualinsight/2016/11/15/bunimovich-stadium/).