Infinitely many coexisting strange attractors
type: Item
instance of: scholarly article
title: Infinitely many coexisting strange attractors
zbMATH Open document ID: 0932.37015
DOI: 10.1016/S0294-1449(98)80001-2
author: Eduardo Colli
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2000-03-19T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78448
review text: The paper deals with an answer to a question in \(C^\infty\) topology and in the context of unfoldings of homoclinic tangencies of surface diffeomorphisms. The author proves that \(C^\infty\) diffeomorphisms of a two-dimensional manifold \(M\) with a homoclinic tangency are in the closure of an open set of \(\text{Diff}^\infty(M)\) containing a dense subset of diffeomorphisms exhibiting infinitely many coexisting Hénon-like strange attractors (or repellers). The author performs a renormalization scheme in 2-cycles of periodic points with a heteroclinic tangency. This renormalization is needed to control orbits, which in turn is essential to guarantee space for arbitrary small \(C^r\) perturbations, for any \(r\geq 0\).
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 37C29
Mathematics Subject Classification ID: 37C75
zbMATH DE Number: 1199909
zbMATH Keywords: homoclinic tangency
zbMATH Keywords: unfoldings
zbMATH Keywords: Hénon-like strange attractor
zbMATH Keywords: heteroclinic tangency
zbMATH Keywords: \(C^r\) perturbation
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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OpenAlex ID: W2029423274
description: scientific article; zbMATH DE number 1199909