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Numerische Mathematik

, Volume 75, Issue 3, pp 293–317 | Cite as

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

  • Michael Dellnitz
  • Andreas Hohmann

Summary.

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.

Mathematics Subject Classification (1991): 65L05, 65L70, 58F15, 58F12 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Michael Dellnitz
    • 1
  • Andreas Hohmann
    • 2
  1. 1.Institut für Angewandte Mathematik, Universität Hamburg, D-20146 Hamburg, GermanyDE
  2. 2.Konrad-Zuse-Zentrum für Informationstechnik Berlin, D-10711 Berlin, GermanyDE

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