General exponential dichotomies: from finite to infinite time

Document Type: Special issue: Trends in Operators on Banach Spaces


‎Universidade de Lisboa‎, Portugal


‎We consider exponential dichotomies on finite intervals and show that if the constants in the notion of an exponential dichotomy are chosen appropriately and uniformly on those intervals‎, ‎then there exists an exponential dichotomy on the whole line‎. ‎We consider the general case of a nonautonomous dynamics that need not be invertible‎. ‎Moreover‎, ‎we consider both cases of discrete and continuous time‎.