random invariant set
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2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Gang Wang ◽  
Yanbin Tang

We prove an abstract result on random invariant sets of finite fractal dimension. Then this result is applied to a stochastic semilinear degenerate parabolic equation and an upper bound is obtained for the random attractors of fractal dimension.


2006 ◽  
Vol 85 (2) ◽  
pp. 269-294 ◽  
Author(s):  
José A. Langa ◽  
James C. Robinson

2001 ◽  
Vol 01 (01) ◽  
pp. 113-126 ◽  
Author(s):  
HANS CRAUEL

Given a differentiable random dynamical system on a finite-dimensional differentiable manifold with a compact random invariant set, we show that there exists an ergodic invariant measure, supported by the invariant set, such that the leading Lyapunov exponent associated with this invariant measure equals the uniform Lyapunov exponent with respect to the invariant set. This is extended to sums of Lyapunov exponents and to the Lyapunov dimension of the set.


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