Topological Methods in Nonlinear Analysis

Nonautonomous Conley index theory the connecting homomorphism

Axel Jänig

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Abstract

Attractor-repeller decompositions of isolated invariant sets give rise to so-called connecting homomorphisms. These homomorphisms reveal information on the existence and strucuture of connecting trajectories of the underlying dynamical system.

To give a meaningful generalization of this general principle to nonautonomous problems, the nonautonomous homology Conley index is expressed as a direct limit. Moreover, it is shown that a nontrivial connecting homomorphism implies, on the dynamical systems level, a sort of uniform connectedness of the attractor-repeller decomposition.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 53, Number 2 (2019), 427-446.

Dates
First available in Project Euclid: 10 May 2019

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1557453830

Digital Object Identifier
doi:10.12775/TMNA.2019.006

Mathematical Reviews number (MathSciNet)
MR3983980

Zentralblatt MATH identifier
07130705

Citation

Jänig, Axel. Nonautonomous Conley index theory the connecting homomorphism. Topol. Methods Nonlinear Anal. 53 (2019), no. 2, 427--446. doi:10.12775/TMNA.2019.006. https://projecteuclid.org/euclid.tmna/1557453830


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