On uniform h-dichotomy of skew-evolution cocycles in Banach spaces

Abstract

The paper presents some characterizations for the study of dichotomy of dynamical systems. Integral characterizations of Datko type are considered for the notion of uniform dichotomy with growth rates, also called uniform h-dichotomy, for skew-evolution cocycles in Banach spaces.

On Dichotomy With Differentiable Growth Rates for Skew-Evolution Cocycles in Banach Spaces

“…Throughout the years an important extension of exponential dichotomy and polynomial dichotomy is introduced by Pinto [16] and it is called dichotomy with growth rates or h-dichotomy, where the growth rate is a nondecreasing and bijective function h : R + → [1, ∞). For recent contributions we refer to the works of Bento, Lupa, Megan and Silva [2], Mihit ¸, Borlea and Megan [14], Gȃinȃ [9], Megan and Gȃinȃ [13].…”