论文标题
环形台球的椭圆岛的双曲线和丰度
Hyperbolicity and Abundance of Elliptical Islands in Annular Billiards
论文作者
论文摘要
我们研究了两个十分位圆圈之间环形表中的台球动力学。随着内圆的中心和半径变化，两个参数图由轨迹向障碍物的首次返回来定义。从豪斯多夫（Hausdorff）距离的意义上讲，我们获得了越来越多的双曲线集，因为半径为零，障碍物的中心近似于外部边界。这些集合中的每个集合的动力学都与越来越多的符号相连。我们还表明，对于许多参数，该系统提出了二次同层面的切线，其分叉产生了椭圆形岛（保守的Newhouse现象）。因此，对于许多参数，我们获得了带有许多椭圆岛的“大”双曲线集的共存。
We study the billiard dynamics in annular tables between two excentric circles. As the center and the radius of the inner circle change, a two parameters map is defined by the first return of trajectories to the obstacle. We obtain an increasing family of hyperbolic sets, in the sense of the Hausdorff distance, as the radius goes to zero and the center of the obstacle approximates the outer boundary. The dynamics on each of these sets is conjugate to a shift with an increasing number of symbols. We also show that for many parameters the system presents quadratic homoclinic tangencies whose bifurcation gives rise to elliptical islands (Conservative Newhouse Phenomenon). Thus, for many parameters we obtain the coexistence of a "large" hyperbolic set with many elliptical islands.
