We investigate some statistical properties of escaping particles in a billiard system whose boundary is described by two control parameters with a hole on its boundary. Initially, we analyze the survival probability for different hole positions and sizes. We notice the survival probability follows an exponential decay with a characteristic power law tail when the hole is positioned partially or entirely over large stability islands in phase space. We find the survival probability exhibits scaling invariance with respect to the hole size. In contrast, the survival probability for holes placed in predominantly chaotic regions deviates from the exponential decay. We introduce two holes simultaneously and investigate the complexity of the escape basins for different hole sizes and control parameters by means of the basin entropy and the basin boundary entropy. We find a non-trivial relation between these entropies and the system's parameters and show that the basin entropy exhibits scaling invariance for a specific control parameter interval.
H ${\acute{e}}$ non [8]使用倾斜台球来研究在卫星相遇和其他情况下发生的混沌散射的方面。他的模型由一个分段映射组成，描述了一个点粒子在两个圆盘上弹性弹跳的运动。从给定的高度出发，得到了一个单参数的轨道族，称为h-轨道。我们得到的逃逸分布的h-轨道的解析表达式，这也是从数值模拟的结果进行比较。最后，讨论了h轨道在Hill问题中的可能应用。
Adiabatic confinement and escape in an open billiard
São Paulo State University (UNESP)（圣保罗州立大学）；Institute of Geosciences and Exact Sciences（地球科学与精确科学学院）；University of São Paulo（圣保罗大学）；Institute of Physics（物理研究所）；Federal University of Paraná（巴拉那联邦大学）
Quantifying intermittency in the open drivebelt billiard
一个“传动带”球场台球与边界组成的圆弧不同半径连接其共同的切线与传统的“直”球场，包括双曲性和混合，以及由于边际不稳定的周期轨道（MUPO）的不稳定性的许多属性。有趣的是，直边和曲边的作用是相反的。本文从台球中的洞逃逸的角度讨论了混沌轨道的间歇性，给出了生存概率$P(t)$的精确的首阶系数$\lim_{t\to\infty} t P(t)$，它是固定洞大小的代数.然而，在小孔尺寸与时间成反比的自然缩放极限中，衰减保持指数。直线和传动带视距之间的最大区别是，在传动带的情况下，有多个家庭的MUPO导致定性的新效果。另一个不同之处在于，在这个系统中，大多数边缘周期轨道都倾斜于边界，从而允许利用全内反射的应用，如微激光器。
