Hans Crauel

Attractors for random dynamical systems

SummaryA criterion for existence of global random attractors for RDS is established. Existence of invariant Markov measures supported by the random attractor is proved. For SPDE this yields invariant measures for the associated Markov semigroup. The results are applied to reation diffusion equations with additive white noise and to Navier-Stokes equations with multiplicative and with additive white noise.

Stabilization of Linear Systems by Noise

It is proved that the biggest Lyapunov number

Additive Noise Destroys a Pitchfork Bifurcation

\lambda _{\max }

Global random attractors are uniquely determined by attracting deterministic compact sets

of the system

AN INTRODUCTION TO INFINITE ERGODIC THEORY (Mathematical Surveys and Monographs 50)

\dot x = (A + F(t))x

Markov measures for random dynamical systems

, where A is a fixed

Hausdorff Dimension of Invariant Sets for Random Dynamical Systems

d \times d

Iterated Function Systems and Multiplicative Ergodic Theory

matrix and

The effect of noise on the Chafee-Infante equation : a nonlinear case study

F(t)

Extremal exponents of random dynamical systems do not vanish

is a zero mean strictly stationary matrix-valued stochastic process, satisfies