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This article is cited in 1 scientific paper (total in 1 paper)
Admissibility and Nonuniform Exponential Trichotomies
Luis Barreiraa, Davor Dragičevićb, Claudia Vallsa a Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001, Lisboa, Portugal
b Department of Mathematics, University of Rijeka, 51000, Rijeka, Croatia
Abstract:
For a nonautonomous dynamics defined by a sequence of linear operators acting on a Banach space, we show that the notion of a nonuniform exponential trichotomy can be completely characterized in terms of admissibility properties. This refers to the existence of bounded solutions under any bounded time-dependent perturbation of certain homotheties of the original dynamics. We also consider the more restrictive notion of a strong nonuniform exponential trichotomy and again we give a characterization in terms of admissibility properties. We emphasize that both notions are ubiquitous in the context of ergodic theory. As a nontrivial application, we show in a simple manner that the two notions of trichotomy persist under sufficiently small linear perturbations. Finally, we obtain a corresponding characterization of nonuniformly partially hyperbolic sets.
Keywords:
exponential trichotomy, robustness, partially hyperbolic set.
Received: 10.11.2014 Accepted: 24.12.2014
Citation:
Luis Barreira, Davor Dragičević, Claudia Valls, “Admissibility and Nonuniform Exponential Trichotomies”, Regul. Chaotic Dyn., 20:1 (2015), 49–62
Linking options:
https://www.mathnet.ru/eng/rcd57 https://www.mathnet.ru/eng/rcd/v20/i1/p49
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Abstract page: | 335 | References: | 44 |
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