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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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