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

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 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