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

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.
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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