Invariant manifolds for stochastic partial differential equations

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