Email this article Emergence and non-typicality of the finiteness of the attractors in many topologies
- Authors: Berger P.1
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Affiliations:
- Laboratoire Analyse, Géométrie et Applications, CNRS (UMR 7539)
- Issue: Vol 297, No 1 (2017)
- Pages: 1-27
- Section: Article
- URL: https://journals.rcsi.science/0081-5438/article/view/174560
- DOI: https://doi.org/10.1134/S0081543817040010
- ID: 174560
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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 Cd-families of Cr-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.
About the authors
Pierre Berger
Laboratoire Analyse, Géométrie et Applications, CNRS (UMR 7539)
Author for correspondence.
Email: berger@math.univ-paris13.fr
France, 99 Ave. Jean-Baptiste Clément, Villetaneuse, 93 430
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