engleski

A version of a theorem of Pliss for nonuniform and noninvertible dichotomies

For a dynamics on the whole line, both for discrete and continuous time, we extend a result of Pliss that gives a characterization of the notion of a trichotomy in various directions. More precisely, the result gives a characterization in terms of an admissibility property in the whole line (namely, the existence of bounded solutions of a linear dynamics under any nonlinear bounded perturbation) of the existence of a trichotomy, that is, of exponential dichotomies in the future and in the past, together with a certain transversality condition at time zero. In particular, we consider arbitrary linear operators acting on a Banach space as well as sequences of norms instead of a single norm, which allows considering the general case of a nonuniform exponential behavior.

exponential dichotomies ; exponential trichotomies

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