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Bifurcations and stability of families of diffeomorphisms

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, University of North Carolina, 27514, Chapel Hill, NC, U.S.A.

    S. Newhouse, J. Palis & F. Takens

  2. I.M.P.A., Rua L. de Camões 68, Rio de Janeiro, Brazil

    S. Newhouse, J. Palis & F. Takens

  3. Department of Mathematics, University of Groningen, Holland

    S. Newhouse, J. Palis & F. Takens

Authors
  1. S. Newhouse
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  2. J. Palis
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  3. F. Takens
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Newhouse, S., Palis, J. & Takens, F. Bifurcations and stability of families of diffeomorphisms. Publications Mathématiques de L’Institut des Hautes Scientifiques 57, 5–71 (1983). https://doi.org/10.1007/BF02698773

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  • DOI: https://doi.org/10.1007/BF02698773

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