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Emergence and non-typicality of the finiteness of the attractors in many topologies

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Abstract

We introduce the notion of emergence for a dynamical system and conjecture the local typicality of super complex ones. Then, as part of this program, we provide sufficient conditions for an open set of C d-families of C r-dynamics to contain a Baire generic set formed by families displaying infinitely many sinks at every parameter, for all 1 ≤ d ≤ r ≤ ∞ and d < ∞ and two different topologies on families. In particular, the case d = r = 1 is new.

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Authors and Affiliations

  1. Laboratoire Analyse, Géométrie et Applications, CNRS (UMR 7539), Université Paris 13, Université Sorbonne Paris Cité, 99 Ave. Jean-Baptiste Clément, 93 430, Villetaneuse, France

    Pierre Berger

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  1. Pierre Berger
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Correspondence to Pierre Berger.

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Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2017, Vol. 297, pp. 7–37.

In memoriam of Dmitry Victorovich Anosov

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Berger, P. Emergence and non-typicality of the finiteness of the attractors in many topologies. Proc. Steklov Inst. Math. 297, 1–27 (2017). https://doi.org/10.1134/S0081543817040010

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