偏心环形开放台球中粒子逃逸动力学的分形性质

二维台球体系因为能够体现混沌现象的基本特征且数值运算相对简单,从而成为研究微观体系混沌动力学的理想模型,近年来一直广受关注.本文研究非同心的环形开放台球中粒子逃逸的混沌动力学性质,它体现了与初条件密切相关的奇异性.采用简化的盒计数 (box-counting)算法,计算了分形维数,结果定量地反映了粒子逃逸前与环壁碰撞次数随粒子入射角变化的函数关系.其中,特别关注环形台球的偏心率对体系混沌性质的影响.

Fractal analysis of escape properties of a non-concentric annular open billiard

Two-dimensional (2D) billiard systems have been a popular subject for its simple numerical computations and the ability to exhibit the full range of chaotic properties. In this work, we study chaotic properties in the particle escape of an open non-concentric annular billiard which manifest the singularities embedded in a subset of all possible initial conditions. Based on a simplified box-counting method we calculate the fractal dimension. The fractal dimensions obtained well demonstrate the numbers of collision of the particle before exiting from the open ranges as a function of the incident angles. We pay particularly attention to the effects of eccentricity of the non-concentric annular billiard on its chaotic behaviors.