Leray functor and orbital Conley index for non-invariant sets

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July 1999, 5(3): 617-630. doi: 10.3934/dcds.1999.5.617

Leray functor and orbital Conley index for non-invariant sets

1.	Department of Mathematics, SUNY at Buffalo, Buffalo, NY 14214, United States

Received November 1997 Revised January 1999 Published May 1999

Abstract
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An orbital Conley index for non-invariant compact sets of discrete-time dynamical systems is introduced. The construction of this new index uses an algebraic reduction process inspired from Leray. Applications to detection of periodic orbits and chaos are presented.

Keywords: Conley index, shift dynamics., leray functor, periodic orbit.

Mathematics Subject Classification: Primary: 58F35, 34C35, 54H2.

Citation: Marian Gidea. Leray functor and orbital Conley index for non-invariant sets. Discrete & Continuous Dynamical Systems - A, 1999, 5 (3) : 617-630. doi: 10.3934/dcds.1999.5.617

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