A lower bound on the Hausdorff dimension of random attractors

  • Markus Böhm (FSU Jena)
E1 05 (Leibniz-Saal)


We consider an SPDE with a Lipschitz continuous nonlinearity driven by a multiplicative noise. Its mild solution generates a random dynamical system and we discuss the existence of a random attractor. Applying a cut-off function to the nonlinearity we obtain a local unstable manifold for the random dynamical system. The local unstable manifold contains an open subset which lies also in the related random attractor. This subset is used to obtain a lower bound on the Hausdorff dimension of the random attractor.

Katja Heid

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Benjamin Gess

Max-Planck-Institut für Mathematik in den Naturwissenschaften