Abstract
We introduce a class of representable sets which is closed under the operations of set theoretical union, intersection, difference, and topological interior and closure. We use this class to construct an algorithm which verifies if for a given dynamical system a given set is an isolating neighborhood. In the case of a positive answer the algorithm constructs an index pair.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Galias, Z., and Zgliczyński, P. (1998). A computer assisted proof of chaos in the Lorenz equations. Physica D 115, 165–188.
Kaczyński, T. and Mrozek, M. (1995). Conley index for discrete multivalued dynamical systems. Topol. Its Appl. 65, 83–96.
Mischaikow, K., and Mrozek, M. (1995). Isolating neighborhoods and chaos. Jap. J. Ind. Appl. Math. 12, 205–236.
Mischaikow, K., and Mrozek, M. (1995). Chaos in Lorenz equations: A computer assisted proof. Bull. Am. Math. Soc. (N.S.) 33, 66–72.
Mrozek, M. (1996). Topological invariants, multivalued maps and computer assisted proofs in dynamics. Comput. Math. 32, 83–104.
Szymczak, A. A combinatorial procedure for finding isolating neighborhoods and index pairs. Proc. Roy. Soc. Edinburgh Ser. A (in press).
Zgliczyński, P. (1997). Computer assisted proof of chaos in the Hénon map and in the Rössler equations. Nonlinearity 10, 243–252.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mrozek, M. An Algorithmic Approach to the Conley Index Theory. Journal of Dynamics and Differential Equations 11, 711–734 (1999). https://doi.org/10.1023/A:1022615629693
Issue Date:
DOI: https://doi.org/10.1023/A:1022615629693