Abud C Vieira, de Carvalho R Egydio
Univ Estadual Paulista-UNESP, 13506-900 Rio Claro, SP, Brazil and Universidade de São Paulo-USP, 05315-970 São Paulo, SP, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Oct;88(4):042922. doi: 10.1103/PhysRevE.88.042922. Epub 2013 Oct 29.
We identify the fine structure of resonance islands and the stickiness in chaos through recurrence time statistics (RTS), which is based on the concept of Poincaré recurrences. The projection of recurrence time statistics onto the phase space does give relevant information on the hierarchical and microstructures of the chaotic beach around the islands of a near-integrable system, the annular billiard. These microstructures interfere in the effective transport of a particle in the phase space, which can be observed through RTS. This technique proves also to be a powerful tool to describe the homoclinic tangle of the manifolds within the chaotic sea.
我们通过基于庞加莱回归概念的回归时间统计（RTS）来识别共振岛的精细结构和混沌中的粘性。将回归时间统计投影到相空间确实能给出关于近可积系统环形台球中岛周围混沌区域的层次结构和微观结构的相关信息。这些微观结构会干扰粒子在相空间中的有效输运，这可以通过RTS观察到。该技术也被证明是描述混沌海中流形的同宿缠结的有力工具。
