A version of a theorem of Pliss for non-uniform and non-invertible dichotomies

作者：Barreira Luis^*; Dragicevic Davor; Valls Claudia

来源：Proceedings of the Royal Society of Edinburgh: Section A Mathematics , 2017, 147(2): 225-243.

DOI：10.1017/S0308210516000123

• exponential dichotomies
• exponential trichotomies
• admissibility

For a dynamics on the whole line, for both 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, i. e. 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 us to consider the general case of non-uniform exponential behaviour.

• 出版日期2017-4