Abstract
In a previous work, the author established a nonautonomous Conley index based on the interplay between a nonautonomous evolution operator and its skew-product formulation. This index is refined to obtain a Conley index for families of nonautonomous evolution operators. Different variants such as a categorial index, a homotopy index and a homology index are obtained. Furthermore, attractor-repeller decompositions and connecting homomorphisms are introduced for the nonautonomous setting.
Citation
Axel Jänig. "Nonautonomous Conley index theory. The homology index and attractor-repeller decompositions." Topol. Methods Nonlinear Anal. 53 (1) 57 - 77, 2019. https://doi.org/10.12775/TMNA.2018.039