Leray Functor and Cohomological Conley Index for Discrete Dynamical Systems
- 1 March 1990
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 318 (1) , 149-178
- https://doi.org/10.2307/2001233
Abstract
We introduce the Leray functor on the category of graded modules equipped with an endomorphism of degree zero and we use this functor to define the cohomological Conley index of an isolated invariant set of a homeomorphism on a locally compact metric space. We prove the homotopy and additivity properties for this index and compute the index in some examples. As one of applications we prove the existence of nonconstant, bounded solutions of the Euler approximation of a certain system of ordinary differential equations.Keywords
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