An Extension of Discrete Lagrangian Descriptors for Unbounded Maps
An Extension of Discrete Lagrangian Descriptors for Unbounded Maps
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无界映射的离散拉格朗日描述符的扩展
DOI：
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发表时间：
2019
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通讯作者：
V. J. García
中科院分区：
文献类型：
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作者：
V. J. García
本文将离散拉格朗日描述子方法推广到无界映射的相空间中。关键思想是构建一个工作定义，该定义建立在Lopesino et al.（2015）中引入的原始方法的基础上，并且依赖于当它们的轨道离开平面中的某个区域时停止初始条件的迭代。这个准则部分地受到动力系统理论中使用的经典分析的启发，该分析通过逃逸时间图来研究映射的动力学。我们说明了这种技术的能力，揭示了几何模板的稳定和不稳定的不变流形在相空间中，也是复杂的结构的混沌集和奇怪的吸引子，通过应用它来揭开一个著名的离散时间系统，Henon映射的相空间。
In this paper we provide an extension for the method of Discrete Lagrangian Descriptors with the purpose of exploring the phase space of unbounded maps. The key idea is to construct a working definition, that builds on the original approach introduced in Lopesino et al. (2015), and which relies on stopping the iteration of initial conditions when their orbits leave a certain region in the plane. This criterion is partly inspired by the classical analysis used in Dynamical Systems Theory to study the dynamics of maps by means of escape time plots. We illustrate the capability of this technique to reveal the geometrical template of stable and unstable invariant manifolds in phase space, and also the intricate structure of chaotic sets and strange attractors, by applying it to unveil the phase space of a well-known discrete time system, the Henon map.