双曲台球的完全双曲性

Hyperbolicity of asymmetric lemon billiards

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 $Γ_r$ is a major arc and $R$ is large. In this paper we prove this conjecture for sufficiently large $R$.

Uniform hyperbolicity in nonflat billiards

Uniform hyperbolicity is a strong chaotic property which holds, in particular, for Sinai billiards. In this paper, we consider the case of a nonflat billiard, that is, a Riemannian manifold with boundary. Each trajectory follows the geodesic flow in the interior of the billiard, and bounces when it meets the boundary. We give a sufficient condition for a nonflat billiard to be uniformly hyperbolic. As a particular case, we obtain a new criterion to show that a closed surface has an Anosov geodesic flow.

具有不相交平行散射体台球的遍历性假设的证明

Proving The Ergodic Hypothesis for Billiards With Disjoint Cylindric Scatterers

在本文中，我们研究了数学台球的遍历性描述了一个点的均匀运动的一个平坦的环面，从许多，成对不相交，管状邻域的平移subtori（所谓的圆柱形散射体）已被删除。我们证明，每个这样的系统是遍历（实际上，一个伯努利流），除非一个简单的几何障碍遍历。

随机扰动台球系统中的双曲性与遍历性

Hyperbolicity and Ergodicity in Randomly Perturbed Billiard Systems

本文探究小随机扰动下随机台球系统的李雅普诺夫指数与双曲性，发现非圆形椭圆、柠檬台球经扰动后兼具遍历性与双曲性，圆形台球则仅遍历且保持零李雅普诺夫指数，相关结果为受噪动力学系统研究提供新视角。

散焦机制的另一边界：非对称柠檬台球的双曲性

On another edge of defocusing: hyperbolicity of asymmetric lemon billiards

本文证明边界由两条圆弧组成的非对称柠檬形凸台球桌能产生双曲台球，揭示了散焦机制在聚焦组件极为接近时仍可成立的新边界。

环形台球中椭圆岛的双曲性与丰度

Hyperbolicity and Abundance of Elliptical Islands in Annular Billiards

本文研究两偏心圆间环形台球动力学，证明当内圆半径趋于零且圆心趋近外边界时，存在符号数递增的双曲集，并通过二次同宿切分岔产生椭圆岛，揭示大双曲集与椭圆岛共存现象。