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The qualitative properties of local random invariant manifolds for stochasticpartial differential equations with quadratic nonlinearities and multiplicativenoise is studied by a cut off technique. By a detail estimates on the Perronfixed point equation describing the local random invariant manifold, thestructure near a bifurcation is given.

Qualitative Properties of Local Random Invariant Manifolds for SPDEs with Quadratic Nonlinearity