Invariant Manifolds for Stochastic PDE with Fractional Brownian Motion

In this work we study invariant manifolds for stochastic partial differential equations (SPDEs) driven by a fractional Brownian motion with parameter $H > 1/2$. The main ingredient in our analysis is the characterization of a controlled deterministic evolution equation where the invariant sets for the SPDE are precisely those of the controlled system. We provide a complete characterization of a given invariant finite dimensional manifold by means of Nagumo-type conditions.