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Regularity of Invariant Manifolds for Nonuniformly Hyperbolic Dynamics

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For any sufficiently small perturbation of a nonuniform exponential dichotomy, we show that there exist invariant stable manifolds as regular as the dynamics. We also consider the general case of a nonautonomous dynamics defined by the composition of a sequence of maps. The proof is based on a geometric argument that avoids any lengthy computations involving the higher order derivatives. In addition, we describe how the invariant manifolds vary with the dynamics.

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Authors and Affiliations

  1. Departamento de Matemática, Instituto Superior Técnico, 1049-001, Lisboa, Portugal

    L. Barreira & C. Valls

  2. Departamento de Matemática, Universidade da Beira Interior, Rua Marquês d’Ávila e Bolama, 6201-001, Covilhã, Portugal

    C. Silva

Authors
  1. L. Barreira
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  2. C. Silva
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  3. C. Valls
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Correspondence to L. Barreira.

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Barreira, L., Silva, C. & Valls, C. Regularity of Invariant Manifolds for Nonuniformly Hyperbolic Dynamics. J Dyn Diff Equat 20, 281–299 (2008). https://doi.org/10.1007/s10884-007-9088-8

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  • DOI: https://doi.org/10.1007/s10884-007-9088-8

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