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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

Marian Gidea 1,

1. 

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

Received  November 1997 Revised  January 1999 Published  May 1999

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