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

2017/11/13 by Jänig, Axel
#34C99 #35B40 #35B41 #37B30 #37B55 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1711.04631

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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