EAN: 9783319124957

SPRINGERBRIEFS IN MATHEMATICS APPROXIMATION O...

This first volume is concerned with the analytic derivation of explicit formulas for the
leading-order Taylor approximations of (local) stochastic invariant manifolds associated with a
broad class of nonlinear stochastic partial differential equations. These approximations take
the form of Lyapunov-Perron integrals  which are further characterized in Volume II as pullback
limits associated with some partially coupled backward-forward systems. This pullback
characterization provides a useful interpretation of the corresponding approximating manifolds
and leads to a simple framework that unifies some other approximation approaches in the
literature. A self-contained survey is also included on the existence and attraction of
one-parameter families of stochastic invariant manifolds  from the point of view of the theory
of random dynamical systems.

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