Attractor Sets as C1-Manifolds

  • Jack K. Hale
  • Luis T. Magalhães
  • Waldyr M. Oliva
Part of the Applied Mathematical Sciences book series (AMS, volume 47)


It is of some interest to determine when the attractor A(F) is a C1-manifold, since it will then have a particularly simple geometric structure which will facilitate the study of qualitative properties of the flow. Results in this direction can be established through the use of Ck-retractions which are defined as Ck maps γ from a Banach manifold into itself such that γ2 = γ, k ≥ 1.


Variational Equation Compact Manifold Neighborhood Versus Tubular Neighborhood Connected Manifold 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Jack K. Hale
    • 1
  • Luis T. Magalhães
    • 2
  • Waldyr M. Oliva
    • 3
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA
  2. 2.Universidade Tecnica de LisbõaLisbonPortugal
  3. 3.Departmento de Matemática Aplicada, Instituto de Matemática e EstatisticaUniversidade de São PauloSão PauloBrasil

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