The random case of Conley's theorem

الأصل · EN

The well-known Conley's theorem states that the complement of chain recurrent set equals the union of all connecting orbits of the flow ϕ on the compact metric space X, i.e. X-CR(ϕ)= [B(A)-A], where CR(ϕ) denotes the chain recurrent set of ϕ, A stands for an attractor and B(A) is the basin determined by A. 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 ω-limit set of some random pre-attractor surrounding it, and by considering appropriate measurability, in fact we also consider the universal σ-algebra Fᵘ-measurability besides F-measurability, we are able to obtain the random case of Conley's theorem.