Nonuniform hyperbolicity and one-sided admissibility

Luis Barreira; Davor Dragičević; Claudia Valls

doi:10.4171/rlm/732

JournalsrlmVol. 27, No. 2pp. 235–247

Nonuniform hyperbolicity and one-sided admissibility

Luis Barreira
Instituto Superior Técnico, Lisboa, Portugal
Davor Dragičević
University of New South Wales, Sydney, Australia
Claudia Valls
Instituto Superior Técnico, Lisboa, Portugal

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Abstract

For a general one-sided nonautonomous dynamics defined by a sequence of linear operators, we consider the notion of an exponential dichotomy with respect to a sequence of norms and we characterize it completely in terms of the admissibility of bounded solutions. As a nontrivial application, we establish the robustness of the notion under sufficiently small parameterized perturbations. Moreover, we show that if the perturbations are Lipschitz or of class $C^{1}$ on the parameter, then the same happens to the projections onto the stable spaces of the perturbation.

Cite this article

Luis Barreira, Davor Dragičević, Claudia Valls, Nonuniform hyperbolicity and one-sided admissibility. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 27 (2016), no. 2, pp. 235–247

DOI 10.4171/RLM/732