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A combinatorial procedure for finding isolating neighbourhoods and index pairs

Published online by Cambridge University Press:  14 November 2011

Andrzej Szymczak
Andrzej Szymczak
Affiliation:
Georgia Institute of Technology, School of Mathematics, Atlanta, GA 30332-0160, U.S.A. e-mail: andrzej@math.gatech.edu
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Synopsis

We present a purely combinatorial procedure for finding an isolating neighbourhood and an index pair contained in a given set, being a finite union of cubes in Rs. It is applied for a computer-assisted computation of the Conley index of an isolated invariant subset of the Hénon attractor. As a corollary, it is shown that the Hénon attractor contains periodic orbits of all principal periods except for 3 and 5.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 5 , 1997 , pp. 1075 - 1088
Copyright
Copyright © Royal Society of Edinburgh 1997

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