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Applications of Admissibility

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Admissibility and Hyperbolicity

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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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Authors and Affiliations

  1. Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Luís Barreira & Claudia Valls

  2. Department of Mathematics, University of Rijeka, Rijeka, Croatia

    Davor Dragičević

Authors
  1. Luís Barreira
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  2. Davor Dragičević
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  3. Claudia Valls
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Barreira, L., Dragičević, D., Valls, C. (2018). Applications of Admissibility. In: Admissibility and Hyperbolicity. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-90110-7_6

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