复合轨道分解的组成:一种算法

arXiv: Chaotic Dynamics Pub Date : 2014-02-24 DOI:10.15388/na.2015.1.8

J. Mart'in, A. G. G'omez, Mateo Moscoso, Daniel Rodr'iguez-P'erez

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引用次数: 1

摘要

本文导出了一维动力学系统$x_{n+1}=f(x_{n};r)$分岔图中周期轨道的分解，其中$f$为单峰函数。我们证明了一个定理，该定理陈述了复合轨道在其简单组分中分裂的充分必要条件。这个定理的一个推论提供了计算这些轨道的算法。这一过程关闭了在(物理学D, 239:1135—1146,2010)中发起的理论框架。

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Compound orbits break-up in constituents: an algorithm

In this paper decomposition of periodic orbits in bifurcation diagrams are derived in unidimensional dynamics system $x_{n+1}=f(x_{n};r)$, being $f$ an unimodal function. We proof a theorem which states the necessary and sufficient conditions for the break-up of compound orbits in their simpler constituents. A corollary to this theorem provides an algorithm for the computation of those orbits. This process closes the theoretical framework initiated in (Physica D, 239:1135--1146, 2010).

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arXiv: Chaotic Dynamics

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