C^γ Stochastic Center Manifold Theory

Stochastic center manifold theory is one of the fundamental of stochastic bifurcation. The stochastic center manifold will justify focusing mainly onto low dimensional problems and tell us how to reduce higher dimensional systems. [4] gave center manifold theory for random cocycle of c diffeomorphisms, [5] made the existence of center manifold theory on the level of random vector fields. This paper proved the existence of c^γ center manifold and gives reduction principle, an example is illustrated for approximation.