[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j180880

CHARACTERIZATION OF TEMPERED EXPONENTIAL DICHOTOMIES

Barreira, Luis (Departamento de Matematica Instituto Superior Tecnico Universidade de Lisboa)
Rijo, Joao (Departamento de Matematica Instituto Superior Tecnico Universidade de Lisboa)
Valls, Claudia (Departamento de Matematica Instituto Superior Tecnico Universidade de Lisboa)

Publication Information

Journal of the Korean Mathematical Society / v.57, no.1, 2020 , pp. 171-194 More about this Journal

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 applications, we detail the consequences of our results for the class of tempered exponential dichotomies, which are ubiquitous in the context of ergodic theory, and we show that the notion of an exponential dichotomy under sufficiently small parameterized perturbations persists and that their stable and unstable spaces are as regular as the perturbation.

Keywords

Tempered exponential dichotomies; admissible spaces;

Citations & Related Records

Reference

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