Characterization of tempered exponential dichotomies
J. Korean Math. Soc.
Published online July 11, 2019
Luis Barreira, João Rijo, and Claudia Valls
Instituto Superior Técnico
Abstract : For a nonautonomous dynamics defined by a sequence of bounded linear operators on a Banach space, we give a characterization of the existence of an exponential dichotomy with respect to a sequence of norms in terms of the invertibility of a certain linear operator between general admissible spaces. This notion of an exponential dichotomy contains as very special cases the notions of uniform, nonuniform and tempered exponential dichotomies. As an application, we detail the consequences of our results for the class of tempered exponential dichotomies that are ubiquitous in the context of ergodic theory.
Keywords : tempered exponential dichotomies, admissible spaces
MSC numbers : 37D99
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