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Topological techniques for efficient rigorous computation in dynamics

Published online by Cambridge University Press:  15 July 2003

Konstantin Mischaikow
Konstantin Mischaikow
Affiliation:
Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, Atlanta, GA 30332, USA. E-mail: mischaik@math.gatech.edu
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Abstract

We describe topological methods for the efficient, rigorous computation of dynamical systems. In particular, we indicate how Conley's Fundamental Decomposition Theorem is naturally related to combinatorial approximations of dynamical systems. Furthermore, we show that computations of Morse decompositions and isolating blocks can be performed efficiently. We conclude with examples indicating how these ideas can be applied to finite- and infinite-dimensional discrete and continuous dynamical systems.

Type
Research Article
Information
Acta Numerica , Volume 11 , January 2002 , pp. 435 - 477
Copyright
© Cambridge University Press 2002

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