Bifurcations and stability of families of diffeomorphisms

  • S. Newhouse
  • J. Palis
  • F. Takens


We consider one parameter families or arcs of diffeomorphisms. For families starting with Morse-Smale diffeomorphisms we characterize various types of (structural) stability at or near the first bifurcation point. We also give a complete description of the stable arcs of diffeomorphisms whose limit sets consist of finitely many orbits. Universal models for the local unfoldings of the bifurcating periodic orbits (especially saddle-nodes) are established, as well as several results on the global dynamical structure of the bifurcating diffeomorphisms. Moduli of stability related to saddle-connections are introduced.


Periodic Orbit Periodic Point Unstable Manifold Stable Manifold Rotation Number 
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Copyright information

© Publications mathématiques de l’I.H.É.S 1983

Authors and Affiliations

  • S. Newhouse
    • 1
    • 2
    • 3
  • J. Palis
    • 1
    • 2
    • 3
  • F. Takens
    • 1
    • 2
    • 3
  1. 1.Department of MathematicsUniversity of North CarolinaChapel HillU.S.A.
  2. 2.I.M.P.A.Rio de JaneiroBrazil
  3. 3.Department of MathematicsUniversity of GroningenHolland

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