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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2017, Volume 297, Pages 7–37
DOI: https://doi.org/10.1134/S0371968517020017 (Mi tm3843) 		 
This article is cited in 18 scientific papers (total in 18 papers)

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

Pierre Berger

Laboratoire Analyse, Géométrie et Applications, CNRS (UMR 7539), Université Paris 13, Universitée Sorbonne Paris Cité, 99 Ave. Jean-Baptiste Clément, 93 430 Villetaneuse, France
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DOI: https://doi.org/10.1134/S0371968517020017
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 $1\le d\le r\le\infty$ and $d<\infty$ and two different topologies on families. In particular, the case $d=r=1$ is new.
Received: September 1, 2016
English version:
Proceedings of the Steklov Institute of Mathematics, 2017, Volume 297, Pages 1–27
DOI: https://doi.org/10.1134/S0081543817040010
Bibliographic databases:
Document Type: Article
UDC: 517.938
Language: Russian
Citation: Pierre Berger, “Emergence and non-typicality of the finiteness of the attractors in many topologies”, Order and chaos in dynamical systems, Collected papers. On the occasion of the 125th anniversary of the birth of Academician Dmitry Victorovich Anosov, Trudy Mat. Inst. Steklova, 297, MAIK Nauka/Interperiodica, Moscow, 2017, 7–37; Proc. Steklov Inst. Math., 297 (2017), 1–27
Citation in format AMSBIB
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\by Pierre Berger
\paper Emergence and non-typicality of the finiteness of the attractors in many topologies
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\bookinfo Collected papers. On the occasion of the 125th anniversary of the birth of Academician Dmitry Victorovich Anosov
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\vol 297
\pages 7--37
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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