Homoclinic tangencies near cascades of period doubling bifurcations
type: Item
instance of: scholarly article
title: Homoclinic tangencies near cascades of period doubling bifurcations
zbMATH Open document ID: 0912.58025
DOI: 10.1016/S0294-1449(98)80119-4
author: Eleonora Catsigeras
author: Heber Enrich
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 1999-05-05T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78438
review text: This interesting paper shows that Feigenbaum maps in \(\mathbb R^n\) (maps that are accumulated by period doubling bifurcations) are approximable, in the \(C^r\) topology for \(r\) large enough, by maps with homoclinic tangencies. To obtain this result, the authors generalize the renormalization theory of \textit{A. M. Davie} [Commun. Math. Phys. 176, No. 2, 261-272 (1996; Zbl 0906.58012)] for \(C^{2 + \varepsilon}\) unimodal maps on the interval, to a renormalization theory in \(\mathbb R^n\) for \(C^r\) maps with \(r\) large enough.
reviewed by: Ale Jan Homburg
Mathematics Subject Classification ID: 37G99
zbMATH DE Number: 1172082
zbMATH Keywords: Feigenbaum maps
zbMATH Keywords: period doubling bifurcations
zbMATH Keywords: homoclinic tangencies
zbMATH Keywords: renormalization
MaRDI profile type: Publication
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Wikidata QID: Q127725510
OpenAlex ID: W2073539287
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description: scientific article; zbMATH DE number 1172082