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This article is cited in 2 scientific papers (total in 2 papers)
Nonuniform Exponential Dichotomies and Lyapunov Functions
Luis Barreiraa, Davor Dragičevićb, Claudia Vallsa a 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.
Received: 10.12.2016 Accepted: 30.03.2017
Citation:
Luis Barreira, Davor Dragičević, Claudia Valls, “Nonuniform Exponential Dichotomies and Lyapunov Functions”, Regul. Chaotic Dyn., 22:3 (2017), 197–209
Linking options:
https://www.mathnet.ru/eng/rcd251 https://www.mathnet.ru/eng/rcd/v22/i3/p197
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Abstract page: | 250 | References: | 33 |
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