Invariant foliations for stochastic dynamical systems with multiplicative stable Levy noise

Abstract

This work concerns the dynamics of a class of stochastic dynamical systems with a multiplicative non-Gaussian Levy noise. We first establish the existence of stable and unstable foliations for this kind of system via the Lyapunov-Perron method. Then we examine the geometric structure of the invariant foliations, and their relation with invariant manifolds. Also we illustrate our results in an example.

Keywords

• Stochastic differential equation
• random dynamical system
• invariant foliation
• invariant manifold
• geometric structure