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Journal of Dynamics and Differential Equations

, Volume 6, Issue 4, pp 631–637 | Cite as

The index of lyapunov stable fixed points in two dimensions

  • E. N. Dancer
  • R. Ortega
Article

Abstract

In this paper, we prove that a stable isolated fixed point of an orientation preserving local homeomorphism onR2 has fixed point index 1. We also give a number of applications to differential equations. In particular, we deduce that a number of existence methods for producing periodic solutions of differential equations in the plane always produce unstable solutions.

Key words

stability fixed point index periodic solutions 

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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • E. N. Dancer
    • 1
  • R. Ortega
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of SydneySydneyAustralia
  2. 2.Departamento de Matemática AplicadaUniversidad de GranadaGranadaSpain

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