Roughness of tempered exponential dichotomies for infinite-dimensional random difference equations. (English) Zbl 1304.37034

Zhou, Linfeng; Lu, Kening; Zhang, Weinian

J. Differ. Equations 254, No. 9, 4024-4046 (2013).

The authors study the roughness of the tempered exponential dichotomies for linear random dynamical systems in Banach spaces. They prove the roughness without assuming their invertibility and the integrability condition of the multiplicative ergodic theorem. They give an explicit bound for the linear perturbation such that the dichotomy is persistent. They also obtain explicit forms for the exponent and the bound of the tempered exponential dichotomy of the perturbed random system in terms of the original ones and the perturbations.

Reviewer: Yan-Hui Qu (Beijing)

MSC:

37H15	Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents
34D09	Dichotomy, trichotomy of solutions to ordinary differential equations

Keywords:

random dynamical system; tempered exponential dichotomy; roughness; cocycle