One-sided dichotomies versus two-sided dichotomies: arbitrary growth rates

Abstract

We obtain necessary and sufficient conditions for the existence of two- sided nonuniform exponential dichotomies with arbitrary growth rates in terms of the existence of one-sided nonuniform exponential dichotomies on the past and on the future. We consider both linear nonautonomous dynamics with discrete and continuous time, on an arbitrary Banach space.

Keywords: Growth rates, nonuniform exponential dichotomies