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ArticleOriginal scientific text

Title

Reconstructing the global dynamics of attractors via the Conley index

Authors 1

Affiliations

  1. Institute for Dynamics, Department of Mathematics, University of Cincinnati, P.O. Box 210025, Cincinnati, Ohio 45221-0025, U.S.A.

Abstract

Given an unknown attractor in a continuous dynamical system, how can we discover the topology and dynamics of ? As a practical matter, how can we do so from only a finite amount of information? One way of doing so is to produce a semi-conjugacy from onto a model system whose topology and dynamics are known. The complexity of then provides a lower bound for the complexity of . The Conley index can be used to construct a simplicial model and a surjective semi-conjugacy for a large class of attractors. The essential features of this construction are that the model can be explicitly described; and that the finite amount of information needed to construct it is computable.

Keywords

ENG
Conley index, semi-conjugacy, simplicial complex, attractor

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Banach Center Publications
1999/47/1
Export to PBN, Opens in new tab
Pages:
145-156
Main language of publication
English
Published
1999
Exact and natural sciences