Retarded Functional Differential Equations on Manifolds

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

Abstract

Let M be a separable C finite dimensional connected manifold, I the closed interval [−r, 0], r > 0, and C0(I, M) the totality of continuous maps ϕ of I into M. Let TM be the tangent bundle of M and τM: TM → M its C-canonical projection. Assume there is given on M a complete Riemannian structure (it exists because M is separable) with δM the associated complete metric. This metric on M induces an admissible metric on C0(I, M) by
$$\delta (\varphi ,\bar \varphi ) = \sup \{ {\delta _M}(\varphi (\theta ),\bar \varphi (\theta )):\theta \in I\} .$$

Keywords

Banach Space Tangent Bundle Functional Differential Equation Tubular Neighborhood Continuous Semigroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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