Celebratio Mathematica — Williams

An Autobiography

Works connected to Stephen Smale

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R. F. Williams: “Classification of one dimensional attractors,” pp. 341–361 in Global analysis (Berkeley, CA, 1–26 July 1968). Edited by S.-S. Chern and S. Smale. Proceedings of Symposia in Pure Mathematics 14. American Mathematical Society (Providence, RI), 1970. MR 266227 Zbl 0213.50401 incollection

This is a sequel to a paper [1967] in which one dimensional attractors are characterized. Some familiarity with [1967] is assumed. Attractor is meant in the sense of S. Smale; for a general introduction to this subject, see the important paper [Smale 1967]. As this is written, the axioms A and B of Smale [1967, pp. 777–778] have been shown to be nongeneric by Abraham and Smale [1970]. Thus the formulation of Smale (sometimes called Anosov–Smale systems or diffeomorphisms) will have to be varied again. But for technical reasons, the example of Abraham and Smale does not directly affect work done on attractors. Moreover, the analysis carried out here and in [1967] does concern an open set of diffeomorphisms, and thus will be pertinent to any formulation of this theory.

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S. Smale and R. F. Williams: “The qualitative analysis of a difference equation of population growth,” J. Math. Biol. 3 : 1 (1976), pp. 1–4. MR 414147 Zbl 0342.92014 article