Hausdorff dimension of a random invariant set |
| |
Authors: | A Debussche |
| |
Institution: | CNRS et Université Paris-Sud. URA 760, Bât. 425, Université de Paris-Sud. 91405 Orsay cedex, France |
| |
Abstract: | The notion of random attractor for a dissipative stochastic dynamical system has recently been introduced. It generalizes the concept of global attractor in the deterministic theory. It has been shown that many stochastic dynamical systems associated to a dissipative partial differential equation perturbed by noise do possess a random attractor. In this paper, we prove that, as in the case of the deterministic attractor, the Hausdorff dimension of the random attractor can be estimated by using global Lyapunov exponents. The result is obtained under very natural assumptions. As an application, we consider a stochastic reaction-diffusion equation and show that its random attractor has finite Hausdorff dimension. |
| |
Keywords: | Attractor stochastic partial differential equation Hausdorff dimension Lyapunov exponents |
本文献已被 ScienceDirect 等数据库收录! |
|