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Synchronization, Lyapunov exponents and stable manifolds for random dynamical systems

by Isabell Vorkastner, Michael Scheutzow




Stochastic Partial Differential Equations and Related Fields


During the past decades, the question of existence and properties of a random attractor of a random dynamical system generated by an S(P)DE has received considerable attention, for example by the work of Gess and Röckner. Recently some authors investigated sufficient conditions which guarantee synchronization, i.e. existence of a random attractor which is a singleton. It is reasonable to conjecture that synchronization and negativity (or non-positivity) of the top Lyapunov exponent of the system should be closely related since both mean that the system is contracting in some sense.


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