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Applications of Admissibility

  • Luís Barreira
  • Davor Dragičević
  • Claudia Valls
Chapter
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Abstract

In this chapter we describe various applications of the results in the former chapters. In particular, we establish the robustness property of an exponential dichotomy by showing that its stability persists under sufficiently small linear perturbations. Moreover, we develop a characterization of hyperbolic sets in terms of an appropriate admissibility property for both maps and flows. Furthermore, we discuss applications of the Pliss type theorems to shadowing and its relation to structural stability. Finally, we obtain a complete characterization of an exponential dichotomy in terms of the existence of a Lyapunov sequence. We do not strive to present the most general results so that one can avoid accessory technicalities.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Luís Barreira
    • 1
  • Davor Dragičević
    • 2
  • Claudia Valls
    • 1
  1. 1.Departamento de Matemática, Instituto Superior TécnicoUniversidade de LisboaLisboaPortugal
  2. 2.Department of MathematicsUniversity of RijekaRijekaCroatia

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