Persistence of the Feigenbaum attractor in one-parameter families
type: Item
instance of: scholarly article
title: Persistence of the Feigenbaum attractor in one-parameter families
zbMATH Open document ID: 0983.37046
author: Eleonora Catsigeras
author: Heber Enrich
published in: Communications in Mathematical Physics
publication date: 2000-11-20T00:00:00Z
review text: The paper deals with the question whether, far away from the fixed map, a whole open set of transformations exhibiting Feigenbaum attractors can exist and whether or not these attractors can always be destroyed by arbitrary small perturbations. Indeed consider a map \(\psi_0\) of class \(C^r\) for large \(r\) of a manifold of dimension \(n\) greater than or equal to 2 having a Feigenbaum attractor. The authors prove that any such \(\psi_0\) is a point of a local codimension-one manifold of \(C^r\) transformations also exhibiting Feigenbaum attractors. As a result, the attractor persists when perturbing a one-parameter family transversal to that manifold at \(\psi_0\). Moreover the authors, using their construction, prove a conjecture by J. Palis stating that a map exhibiting a Feigenbaum attractor can be perturbed to obtain homoclinic tangencies.
Mathematics Subject Classification ID: 37E20
Mathematics Subject Classification ID: 37G25
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 37C05
Mathematics Subject Classification ID: 37C29
zbMATH DE Number: 1533562
zbMATH Keywords: Feigenbaum attractor
zbMATH Keywords: small \(C^r\) perturbation
zbMATH Keywords: homoclinic tangencies
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: s002200050739
OpenAlex ID: W2111162345
DOI: 10.1007/S002200050739
description: scientific article; zbMATH DE number 1533562