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arXiv · 1711.04631

Nonautonomous Conley Index Theory: The Homology Index and Attractor-Repeller decompositions

Axel Jänig
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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 conecting homomorphisms are introduced for the nonautonomous setting.

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Axel Jänig. 2017-11-13. Nonautonomous Conley Index Theory: The Homology Index and Attractor-Repeller decompositions. https://arxiv.org/abs/1711.04631

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