This article is cited in 2 papers

Nonuniform Exponential Dichotomies and Lyapunov Functions

Luis Barreira^a, Davor Dragičević^b, Claudia Valls<sup>a

a</sup> Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
^b School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052, Australia

Abstract: For the nonautonomous dynamics defined by a sequence of bounded linear operators acting on an arbitrary Hilbert space, we obtain a characterization of the notion of a nonuniform exponential dichotomy in terms of quadratic Lyapunov sequences. We emphasize that, in sharp contrast with previous results, we consider the general case of possibly noninvertible linear operators, thus requiring only the invertibility along the unstable direction. As an application, we give a simple proof of the robustness of a nonuniform exponential dichotomy under sufficiently small linear perturbations.

Keywords: nonuniform exponential dichotomies, Lyapunov functions.

MSC: 37D99

Received: 10.12.2016
Accepted: 30.03.2017

Language: English

DOI: 10.1134/S1560354717030017

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