Nonautonomous Conley index theory. Continuation of Morse-decompositions (Q2422553)

In [J. Fixed Point Theory Appl. 19, No. 3, 1825--1870 (2017; Zbl 1379.37033)] the author developed a nonautonomous Conley index theory, and in [Topol. Methods Nonlinear Anal. 53, No. 2, 427--446 (2019; Zbl 1436.37019)] he investigated attractor-repeller pairs and connecting homomorphisms for the associated homology Conley indices. The present paper is a continuation of this work dealing with partially ordered Morse decompositions in the framework of skew-product semiflows. In particular the homology index braid for Morse decompositions is established and the continuation property is proved.