Bibliographical Notes

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


The abstract framework in this section was introduced in Hale [11]. Hale and Lopes [14] (see also Hale [10], Massatt [32, 33]) proved the result in Section 1 that a compact dissipative α-contraction Tf(t) has A(f) compact, Billotti and LaSalle [3] proved the same result for point dissipative maps Tf(t) which are completely continuous for t ≥ r. For some other evolutionary systems which are special cases of the abstract framework in Section 1, see Hale [11], Massatt [34]. For partial results on question Q5, see Chernoff and Marsden [52], Hale and Scheurle [53].


Hopf Bifurcation Unstable Manifold Hausdorff Dimension Abstract Framework Bibliographical Note 
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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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