Compactification at Infinity

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


The behavior at infinity of solutions of ordinary differential equations in the plane was studied by Poincaré by compactification of the Euclidean plane into the unit two-dimensional sphere S2. The same idea of compactification can be applied to RFDEs. In order to illustrate this, we present here a study on equations obtained by compactification of linear delay equations \(\dot x(t) = Ax(t - 1)\) in ℝ2 and in ℝ (compactified to the sphere S2 and the circle S1, respectively).


Periodic Solution Periodic Orbit Hopf Bifurca Imaginary Axis Euclidean Plane 
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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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