Unstable Periodic Orbits in the Stadium Billiard

TL;DR

This paper introduces a numerical method for calculating unstable periodic orbits in the stadium billiard, enabling analysis of chaotic dynamics with applications in semiclassical physics and experimental systems.

Contribution

It presents a systematic numerical approach to find all unstable periodic orbits up to order 11 in the stadium billiard, advancing the understanding of chaotic systems.

Findings

Calculated all periodic orbits up to order 11

Determined average Lyapunov exponent and topological entropy

Applied results to semiclassical quantization and experiments

Abstract

A systematic numerical technique for the calculation of unstable periodic orbits in the stadium billiard is presented. All the periodic orbits up to order $p=11$ are calculated and then used to calculate the average Lyapunov exponent and the topological entropy. Applications to semiclassical quantization and to experiments in mesoscopic systems and microwave cavities are noted.