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This work deals with the dynamics of a class of stochastic dynamical systemswith a multiplicative non-Gaussian Levy noise. We first establish the existenceof stable and unstable foliations for this system via the Lyapunov-Perronmethod. Then we examine the geometric structure of the invariant foliations,and their relation with invariant manifolds. Finally, we illustrate our resultsin an example.

Invariant foliations for stochastic dynamical systems with multiplicative stable Levy noise