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Stability and Genericity in Dynamical Systems

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Abstract

A general reference to this subject, with examples, written about the summer of 1967 is [7], (reported in a recent Bourbaki seminar by C. Godbillon). Here I will try to emphasize developments since. An important source of much of this more recent work should appear in the immediate future in [1].

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References

  1. Global Analysis, Proceedings of the 1968 AMS institute on global analysis at Berkeley. Vol. 1 (of 3 vols) is devoted to dynamical systems.

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  2. R. Bowen, Periodic points and measures for Axiom A diffeomorphisms, Trans. AMS 154 (1971), 377–397.

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  3. R. Bowen, Markov partitions for Axiom A diffeomorphisms, Amer. J. Math. 92 (1970), 725–747.

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  4. J. Guckenheimer, Axiom A + no cycles⇒ ζ f (t) rational, Bull. AMS 76 (1970), 592–594.

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  5. M. Hirsch, J. Pahs, C. Pugh, M. Shub, Neighborhoods of hyperbolic sets, Inventiones Math. 9 (1970), 121–134.

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  6. J. Pahs, On Morse-Smale dynamical systems, Topology 8 (1969), 385–405.

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  7. S. Smale, Differentiable dynamical systems, Bull. AMS 73 (1967), 747–817.

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© 1980 Springer-Verlag New York Inc.

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Smale, S. (1980). Stability and Genericity in Dynamical Systems. In: The Mathematics of Time. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8101-3_3

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  • DOI: https://doi.org/10.1007/978-1-4613-8101-3_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-90519-8

  • Online ISBN: 978-1-4613-8101-3

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