The random case of Conley's theorem: III. Random semiflow case and Morse decomposition

Details The random case of Conley's theorem: III. Random semiflow case and Morse decomposition The random case of Conley's theorem: III. Random semiflow case and Morse decomposition

2007-10-30

arxiv.org/abs/0710.5687v1

Nonlinearity 20 (2007), 2773--2791

Mathematics

Dynamical Systems

21 pages, no figure

Scientific paper

10.1088/0951-7715/20/12/003

In the first part of this paper, we generalize the results of the author \cite{Liu,Liu2} from the random flow case to the random semiflow case, i.e. we obtain Conley decomposition theorem for infinite dimensional random dynamical systems. In the second part, by introducing the backward orbit for random semiflow, we are able to decompose invariant random compact set (e.g. global random attractor) into random Morse sets and connecting orbits between them, which generalizes the Morse decomposition of invariant sets originated from Conley \cite{Con} to the random semiflow setting and gives the positive answer to an open problem put forward by Caraballo and Langa \cite{CL}.

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