• Michèle Audin
  • Mihai Damian
Part of the Universitext book series (UTX)


We define, construct and study pseudo-gradient fields, whose trajectories connect the critical points of a Morse function. These vector fields allow us to define the stable and unstable manifolds of the critical points, which will play an important role. We call attention to the “male property” because of which, for example, there are only finitely many trajectories connecting two critical points with consecutive indices and we prove the existence of pseudo-gradient fields satisfying this property.


Vector Field Unstable Manifold Flow Line Stable Manifold Smale Condition 
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Supplementary material


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Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  • Michèle Audin
    • 1
  • Mihai Damian
    • 1
  1. 1.IRMAUniversité Louis PasteurStrasbourg CedexFrance

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