Hausdorff dimension of a random invariant set
The author proves that, as in the case of the deterministic attractor, the Hausdorff dimension of the random attractor for a dissipative stochastic dynamical system can be estimated by using global Lyapunov exponents. The result is obtained under assumptions that are satisfied by many stochastic dynamical systems originating in dissipative evolution equations. As an application, the author considers a stochastic reaction-diffusion equation and shows that its random attractor has finite Hausdorff dimension.
scientific article; zbMATH DE number 1268421
scientific article