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Fourth International Conference on Dynamic Systems and Applications
May 21-24, 2003
Department of Mathematics, Morehouse College
Atlanta, GA, USA

Organizers
M. Sambandham

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Automatic Computation of the Conley Index. A Cubical Approach
by
Pawel Pilarczyk
Georgia Tech (Atlanta, USA) and Jagiellonian University (Krakow, Poland)
Coauthors: Konstantin Mischaikow and Marian Mrozek

We introduce an automated procedure for the computation of the Conley index of an isolated invariant set in Rn under a dynamical system with discrete time. The Conley index is a robust topological invariant introduced in the 1970s which proved its usefulness in the analysis of invariant sets in dynamical systems in various contexts. Our method for the computation of the Conley index uses sets built of cubes with respect to a uniform grid in Rn (cubical sets) which are easy to implement and manipulate in the computer. Main highlights of our method are: an algorithm for the construction of an index pair, and an algorithm for the computation of relative homology of cubical sets and continuous maps.

Date received: February 27, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cakr-71.