Lagrangian descriptors for two dimensional, area preserving, autonomous and nonautonomous maps

被引:47
作者
Lopesino, Carlos [1 ]
Balibrea, Francisco [1 ]
Wiggins, Stephen [2 ]
Mancho, Ana M. [1 ]
机构
[1] CSIC UAM UC3M UCM, Inst Ciencias Matemat, Madrid 28049, Spain
[2] Univ Bristol, Sch Math, Univ Walk, Bristol BS8 1TW, Avon, England
关键词
Lagrangian descriptor; Chaotic saddle; Autonomous map; Nonautonomous map; LINEARIZATION; DYNAMICS; SYSTEMS;
D O I
10.1016/j.cnsns.2015.02.022
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper we generalize the method of Lagrangian descriptors to two dimensional, area preserving, autonomous and nonautonomous discrete time dynamical systems. We consider four generic model problems - a hyperbolic saddle point for a linear, area-preserving autonomous map, a hyperbolic saddle point for a nonlinear, area-preserving autonomous map, a hyperbolic saddle point for linear, area-preserving nonautonomous map, and a hyperbolic saddle point for nonlinear, area-preserving nonautonomous map. The discrete time setting allows us to evaluate the expression for the Lagrangian descriptors explicitly for a certain class of norms. This enables us to provide a rigorous setting for the notion that the "singular sets" of the Lagrangian descriptors correspond to the stable and unstable manifolds of hyperbolic invariant sets, as well as to understand how this depends upon the particular norms that are used. Finally we analyze, from the computational point of view, the performance of this tool for general nonlinear maps, by computing the "chaotic saddle" for autonomous and nonautonomous versions of the Henon map. (C) 2015 Elsevier B.V. All rights reserved.
引用
收藏
页码:40 / 51
页数:12
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