Hyperbolic structure and stickiness effect: A case of a 2D area-preserving twist mapping
Hyperbolic structure and stickiness effect: A case of a 2D area-preserving twist mapping
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DOI：
10.1007/s11433-013-5299-7
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发表时间：
2012-12
期刊：
影响因子：
--
通讯作者：
Li-Yong Zhou;Jian Li;Jian Cheng;Yi-sui Sun
中科院分区：
文献类型：
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作者：
Li-Yong Zhou;Jian Li;Jian Cheng;Yi-sui Sun
研究了混沌轨道在动力系统相空间中扩散时所受到的粘性效应。以往的研究表明，相空间中的双曲结构在引起粘性效应中起着至关重要的作用。本文研究了粘性效应与双曲结构几何性质之间的关系。以二维保面积扭曲映射为模型，给出了计算双曲周期轨道位置和双曲周期轨道稳定流形与不稳定流形夹角的数值算法.我们展示了粘性效应和轨道扩散速度与角度的关系。
The stickiness effect suffered by chaotic orbits diffusing in the phase space of a dynamical system is studied in this paper. Previous works have shown that the hyperbolic structures in the phase space play an essential role in causing the stickiness effect. We present in this paper the relationship between the stickiness effect and the geometric property of hyperbolic structures. Using a two-dimensional area-preserving twist mapping as the model, we develop the numerical algorithms for computing the positions of the hyperbolic periodic orbits and for calculating the angle between the stable and unstable manifolds of the hyperbolic periodic orbit. We show how the stickiness effect and the orbital diffusion speed are related to the angle.