开放可积台球中的内在粘性：微小边界效应
Intrinsic stickiness in open integrable billiards: tiny border effects
摘要：
通过逃逸时间统计和发射角分析了开可积台球逃逸点的圆化边界效应。该模型是矩形台球和逃逸点的形状被假定为具有半圆形的形式。逃逸时间和发射角度的粘性和自相似结构在“西洋双陆棋”一样的初始条件条纹内产生。这些条纹产生在两个不同发射角但相同逃逸时间之间的边界处。随着舍入效应的增加，西洋双陆棋条纹开始重叠，逃逸时间统计服从幂律衰减，预计会出现异常扩散。微小的圆形边界（大约$0.1\%$从整个台球大小）被证明是足以产生粘性运动，而边界大于$10\%$是足以产生逃逸时间与混沌衰减。
英文摘要：
Rounding border effects at the escape point of open integrable billiards are analyzed via the escape times 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 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 same escape times. As the rounding effects increase, backgammon stripes start to overlap and the escape times statistics obeys the power law decay and anomalous diffusion is expected. Tiny rounded borders (around $0.1\%$ from the whole billiard size) are shown to be sufficient to generate the sticky motion, while borders larger than $10\%$ are enough to produce escape times with chaotic decay.
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