A subdivision algorithm for the computation of unstable manifolds and global attractors

被引:225
作者
Dellnitz, M [1 ]
Hohmann, A [1 ]
机构
[1] KONRAD ZUSE ZENTRUM INFORMAT TECH BERLIN, D-10711 BERLIN, GERMANY
关键词
Mathematics Subject Classification (1991): 65L05, 65L70, 58F15, 58F12;
D O I
10.1007/s002110050240
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Each invariant set of a given dynamical system is part of the global attractor. Therefore the global attractor contains all the potentially interesting dynamics, and, in particular, it contains every (global) unstable manifold. For this reason it is of interest to have an algorithm which allows to approximate the global attractor numerically. In this article we develop such an algorithm using a subdivision technique. We prove convergence of this method in a very general setting, and, moreover, we describe the qualitative convergence behavior in the presence of a hyperbolic structure. The algorithm can successfully be applied to dynamical systems of moderate dimension, and we illustrate this fact by several numerical examples.
引用
收藏
页码:293 / 317
页数:25
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