Davidchack RL, Lai YC, Bollt EM, Dhamala M
Department of Physics and Astronomy, University of Kansas, Lawrence, Kansas 66045, USA.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Feb;61(2):1353-6. doi: 10.1103/physreve.61.1353.
An outstanding problem in chaotic dynamics is to specify generating partitions for symbolic dynamics in dimensions larger than 1. It has been known that the infinite number of unstable periodic orbits embedded in the chaotic invariant set provides sufficient information for estimating the generating partition. Here we present a general, dimension-independent, and efficient approach for this task based on optimizing a set of proximity functions defined with respect to periodic orbits. Our algorithm allows us to obtain the approximate location of the generating partition for the Ikeda-Hammel-Jones-Moloney map.
混沌动力学中的一个突出问题是为大于一维的符号动力学指定生成划分。已知嵌入混沌不变集中的无限多个不稳定周期轨道为估计生成划分提供了足够的信息。在此，我们基于优化一组相对于周期轨道定义的接近度函数，提出了一种通用、与维度无关且高效的方法来完成此任务。我们的算法使我们能够获得池田 - 哈默尔 - 琼斯 - 莫洛尼映射的生成划分的近似位置。
