Theorems of Perron type for uniform exponential dichotomy of linear skew-product semiflows.

Abstract

We study the connections between the uniform exponential dichotomy of a discrete linear skew-product semiflow and the uniform admissibility of the pair $(c_{0}(\n,X),c_{00}(\n, X))$. We give necessary and sufficient conditions for uniform exponential dichotomy of linear skew-product semiflows in terms of the uniform admissibility of the pairs $(c_{0}(\n, X),c_{00}(\n, X))$ and $(C_0(\r, X),$ $C_{00}(\r, X))$, respectively. We generalize a dichotomy theorem due to Van Minh, Räbiger and Schnaubelt for the case of linear skew-product semiflows.