Zaslavsky G. M., Edelman M.
Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, New York 10012Department of Physics, New York University, 2-4 Washington Place, New York, New York 10003.
Chaos. 2001 Jun;11(2):295-305. doi: 10.1063/1.1355358.
We consider chaotic properties of a particle in a square billiard with a horizontal bar in the middle. Such a system can model field-line windings of the merged surfaces. The system has weak-mixing properties with zero Lyapunov exponent and entropy, and it can be also interesting as an example of a system with intermediate chaotic properties, between the integrability and strong mixing. We show that the transport is anomalous and that its properties can be linked to the ergodic properties of continued fractions. The distribution of Poincare recurrences, distribution of the displacements, and the moments of the truncated distribution of the displacements are obtained. Connections between different exponents are found. It is shown that the distribution function of displacements and its truncated moments as a function of time exhibit log-periodic oscillations (modulations) with a universal period T(log)=pi(2)/12 ln 2. We note that similar results are valid for a family of billiard, particularly for billiards with square-in-square geometry. (c) 2001 American Institute of Physics.
我们考虑在中间有一根水平杆的方形台球桌中粒子的混沌特性。这样的系统可以模拟合并表面的磁力线缠绕。该系统具有零李雅普诺夫指数和熵的弱混合特性，并且作为介于可积性和强混合之间具有中间混沌特性的系统示例也可能很有趣。我们表明输运是反常的，并且其特性可以与连分数的遍历特性相关联。得到了庞加莱回归的分布、位移的分布以及位移截断分布的矩。发现了不同指数之间的联系。结果表明，位移的分布函数及其截断矩作为时间的函数呈现出具有通用周期(T(\log)=\pi^2 / 12\ln2)的对数周期振荡（调制）。我们注意到类似的结果对于一类台球桌是有效的，特别是对于具有方中方几何形状的台球桌。(c) 2001美国物理研究所。
