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arXiv · 2412.02093

Twist Coefficients of Periodic Orbits of Minkowski Billiards

Carlos Villanueva·Pengfei Zhang
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Abstract

We investigate the fundamental properties of Minkowski billiards and introduce a new coordinate system $(s,u)$ on the phase space $\mathcal{M}$. In this coordinate system, the Minkowski billiard map $\mathcal{T}$ preserves the standard area form $\omega = ds \wedge du$. We then classify the periodic orbits of Minkowski billiards with period $2$ and derive formulas for the twist coefficient $\tau_1$ for elliptic periodic orbits, expressed in terms of the geometric characteristics of the billiard table. Additionally, we analyze the stability properties of these elliptic periodic orbits.

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Carlos Villanueva, Pengfei Zhang. 2024-12-03. Twist Coefficients of Periodic Orbits of Minkowski Billiards. https://arxiv.org/abs/2412.02093

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