On Another Edge of Defocusing: Hyperbolicity of Asymmetric Lemon Billiards
On Another Edge of Defocusing: Hyperbolicity of Asymmetric Lemon Billiards
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散焦的另一个边缘：不对称柠檬台球的双曲性
DOI：
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发表时间：
2014
影响因子：
2.4
通讯作者：
Pengfei Zhang
中科院分区：
文献类型：
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作者：
L. Bunimovich;Hong;Pengfei Zhang
散焦机制提供了一种通过将台球桌边界的所有规则分量与每个聚焦分量分开足够远来构造具有聚焦分量的混沌(双曲)台球的方法。如果台球桌边界的所有聚焦分量都是圆弧，则上述分离要求归结为通过完成聚焦分量得到的所有圆都包含在台球桌中。本文证明了一类边界由两个圆弧组成的凸表-非对称柠檬生成双曲台球。这一结果相当令人惊讶，因为非对称柠檬桌的聚焦分量彼此非常接近，而且因为这些桌子是40多年前建造的第一个凸形遍历台球的扰动。
Defocusing mechanism provides a way to construct chaotic (hyperbolic) billiards with focusing components by separating all regular components of the boundary of a billiard table sufficiently far away from each focusing component. If all focusing components of the boundary of the billiard table are circular arcs, then the above separation requirement reduces to that all circles obtained by completion of focusing components are contained in the billiard table. In the present paper we demonstrate that a class of convex tables—asymmetric lemons, whose boundary consists of two circular arcs, generate hyperbolic billiards. This result is quite surprising because the focusing components of the asymmetric lemon table are extremely close to each other, and because these tables are perturbations of the first convex ergodic billiard constructed more than 40 years ago.