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A subdivision algorithm for the computation of unstable manifolds and global attractors (1997)

Dellnitz, Michael ; Hohmann, Andreas

Springer

Numerische Mathematik 75 (1997), S. 293-317

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Details

ISSN: 0945-3245

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

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: 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.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/s002110050240

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