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arXiv · 1902.08130

Hyperbolicity of asymmetric lemon billiards

Xin Jin·Pengfei Zhang
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Abstract

Asymmetric lemon billiards was introduced in [CMZZ], where the billiard table $Q(r,b,R)$ is the intersection of two round disks with radii $r\le R$, respectively, and $b$ measures the distance between the two centers. It is conjectured [BZZ] that the asymmetric lemon billiards is hyperbolic when the arc $\Gamma_r$ is a major arc and $R$ is large. In this paper we prove this conjecture for sufficiently large $R$.

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Xin Jin, Pengfei Zhang. 2019-02-21. Hyperbolicity of asymmetric lemon billiards. https://doi.org/10.1088/1361-6544/abaff2

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