Hausdorff dimension of invariant sets for random dynamical systems

被引：58

作者：

Crauel H. ^{[1
]}

Flandoli F. ^{[2
]}

机构：

[1] Fachbereich 3 Mathematik, Sekr. MA 7-4, 10623 Berlin

[2] Dipartimento di Matematica Applicata U. Dini, 56126 Pisa

来源：

Journal of Dynamics and Differential Equations | 1998年 / 10卷 / 3期

关键词：

Hausdorff dimension; Navier-Stokes equation; Random attractor; Random dynamical system; Random invariant set; Reaction diffusion equation;

D O I：

10.1023/A:1022605313961

中图分类号：

学科分类号：

摘要：

Suppose ω→X(ω) is a compact random set, invariant with respect to a continuously differentiable random dynamical system (RDS) on a separable Hilbert space. It is shown that the Hausdorff dimension dim H(X(ω)) is an invariant random variable, and it is bounded by d, provided the RDS contracts d-dimensional volumes exponentially fast. Both exponential decrease of d-volumes as well as the approximation of the RDS by its linearization are assumed to hold uniformly in ωεΩ. The results are applied to reaction diffusion equations with additive noise and to two-dimensional Navier-Stokes equations with bounded real noise. © 1998 Plenum Publishing Corporation.

引用

页码：449 / 474

页数：25

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