The Poincaré Manifold at A Stable Equilibrium of C2 Planar Flow

William Rivera, Richard Sowers

Research output: Contribution to journalArticlepeer-review


We establish the existence of a unique C2 local invariant manifold at the stable equilibrium of a C2 vector field. Here, in contrast to the standard case, the eigenvalue ratio μ/λ is bounded above by the degree of smoothness of the vector field.

Original languageEnglish (US)
Pages (from-to)247-259
Number of pages13
JournalApplicable Analysis
Issue number1-4
StatePublished - Feb 1 1994
Externally publishedYes


  • Poincaré manifold
  • Weak stable manifold
  • generalized center stable manifold
  • local invariant manifold
  • nonresonance inequality
  • strong stable manifold

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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