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arXiv · 2603.00275

Existence of stable periodic orbits in billiards close to lemon and moon billiards

Alexander Grigo
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Abstract

It is known that at lemon and moon billiards that have a sufficiently small curvature on one of their circular arcs are hyperbolic. In this paper we show that replacing this circular arc by a more general boundary component of small curvature could produce billiard tables that admit nonlinearly stable periodic orbits.

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Alexander Grigo. 2026-02-27. Existence of stable periodic orbits in billiards close to lemon and moon billiards. https://arxiv.org/abs/2603.00275

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