Invariant manifolds for stochastic partial differential equations

Details Invariant manifolds for stochastic partial differential equations Invariant manifolds for stochastic partial differential equations

2004-09-24

arxiv.org/abs/math/0409485v1

Annals of Probability 31(2003), 2109-2135

Mathematics

Dynamical Systems

Scientific paper

Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for stochastic ordinary differential equations is relatively mature. In this paper, we present a unified theory of invariant manifolds for infinite dimensional {\em random} dynamical systems generated by {\em stochastic} partial differential equations. We first introduce a random graph transform and a fixed point theorem for non-autonomous systems. Then we show the existence of generalized fixed points which give the desired invariant manifolds.

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