Random Perturbation of Invariant Manifolds for Non-Autonomous Dynamical Systems

Random invariant manifolds are geometric objects useful for understanding dynamics near the random fixed point under stochastic influences. Under framework of a dynamical system, we compared perturbed non-autonomous partial differential equations with original equations. Mainly, derived some pathwise approximation results when Gaussian white noise was replaced by colored noise, which is type Wong–Zakai approximation.