ISSN:
1572-9222
Keywords:
Hausdorff dimension
;
random invariant set
;
random attractor
;
random dynamical system
;
Navier–Stokes equation
;
reaction diffusion equation
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract 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 ωɛΩ. The results are applied to reaction diffusion equations with additive noise and to two-dimensional Navier–Stokes equations with bounded real noise.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1022605313961
