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.
Citation
Axel Jänig. "Nonautonomous Conley index theory the connecting homomorphism." Topol. Methods Nonlinear Anal. 53 (2) 427 - 446, 2019. https://doi.org/10.12775/TMNA.2019.006