Existence, regularity, and a strong Itô formula for the isochronal phase of SPDE

Abstract

We prove the existence and regularity of the isochron map for stable invariant manifolds of a large class of evolution equations. Our results apply in particular to the isochron map of reaction-diffusion equations and neural field equations. Using the regularity properties proven here, we prove a strong Itô formula for the isochronal phase of stochastically perturbed travelling waves and other patterns appearing in SPDEs driven by white noise, even for SPDEs that only admit mild solutions.