Leray functor and orbital Conley index for non-invariant sets

Marian Gidea

doi:10.3934/dcds.1999.5.617

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1999, Volume 5, Issue 3: 617-630. Doi: 10.3934/dcds.1999.5.617

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Leray functor and orbital Conley index for non-invariant sets

Marian Gidea^1,

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

Received: October 31, 1997

Revised: December 31, 1998

Published: June 1999

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Abstract

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.

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Mathematics Subject Classification: Primary: 58F35, 34C35, 54H20.

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