51 research outputs found
The random case of Conley's theorem
The well-known Conley's theorem states that the complement of chain recurrent
set equals the union of all connecting orbits of the flow on the compact
metric space , i.e. , where
denotes the chain recurrent set of , stands for
an attractor and is the basin determined by . In this paper we show
that by appropriately selecting the definition of random attractor, in fact we
define a random local attractor to be the -limit set of some random
pre-attractor surrounding it, and by considering appropriate measurability, in
fact we also consider the universal -algebra -measurability besides -measurability, we are able to obtain
the random case of Conley's theorem.Comment: 15 page
The random case of Conley's theorem: III. Random semiflow case and Morse decomposition
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}.Comment: 21 pages, no figur
CIDS - Cabin Intercommunication Data System
Paper of the Walter Blohm award winners 1987 presented on the occasion of the 100th anniversary of Dipl.-Ing. Walter Blohm, July 28, 1987Copy held by FIZ Karlsruhe; available from UB/TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman
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