Custódio M S, Beims M W
Departamento de Física, Universidade Federal do Paraná, 81531-990 Curitiba, PR, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5 Pt 2):056201. doi: 10.1103/PhysRevE.83.056201. Epub 2011 May 2.
Rounding border effects at the escape point of open integrable billiards are analyzed via the escape-time statistics and emission angles. The model is the rectangular billiard and the shape of the escape point is assumed to have a semicircular form. Stickiness, chaos, and self-similar structures for the escape times and emission angles are generated inside "backgammon" like stripes of initial conditions. These stripes are born at the boundary between two different emission angles but with the same escape times and when rounding effects increase they start to overlap generating a very rich dynamics. Tiny rounded borders (around 0.1% from the whole billiard size) are shown to be sufficient to generate the sticky motion with power-law decay γ(esc)=1.27, while borders larger than 10% are enough to produce escape times related to the chaotic motion. Escape exponents in the interval 1<γ(esc)<2 are generated due to marginal unstable periodic orbits trapping alternately (in time) regular and chaotic trajectories.
通过逃逸时间统计和发射角来分析开放可积台球逃逸点处的圆形边界效应。模型为矩形台球，且假设逃逸点的形状为半圆形。在类似“西洋双陆棋”的初始条件条纹内部，会产生逃逸时间和发射角的粘性、混沌及自相似结构。这些条纹产生于两个不同发射角但逃逸时间相同的边界处，当圆形效应增强时，它们开始重叠，从而产生非常丰富的动力学。微小的圆形边界（约为整个台球尺寸的0.1%）足以产生具有幂律衰减γ(esc)=1.27的粘性运动，而大于10%的边界则足以产生与混沌运动相关的逃逸时间。由于边缘不稳定周期轨道交替（在时间上）捕获规则和混沌轨迹，从而产生了1<γ(esc)<2区间内的逃逸指数。
