Conjugate dynamics on center-manifolds for stochastic partial differential equations.

In this paper, we prove that for a random differential equation with the driving noise constructed from a Q -Wiener process and the Wiener shift, there exists a local center, unstable, stable, center-unstable, center-stable manifold, and a local stable foliation, an unstable foliation on the center-unstable manifold, and a stable foliation on the center-stable manifold, the smoothness of which depend on the vector fields of the equation. Also we show that any two arbitrarily local center manifolds constructed as above are conjugate. [ABSTRACT FROM AUTHOR]