Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Leray functor and cohomological Conley index for discrete dynamical systems

Author: Marian Mrozek
Journal: Trans. Amer. Math. Soc. 318 (1990), 149-178
MSC: Primary 34C35; Secondary 39A10, 55M99, 58F25
MathSciNet review: 968888
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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.

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Keywords: Conley index, Leray endomorphism, isolated invariant set
Article copyright: © Copyright 1990 American Mathematical Society