Saddle-focus singular cycles and prevalence of hyperbolicity
type: Item
instance of: scholarly article
title: Saddle-focus singular cycles and prevalence of hyperbolicity
zbMATH Open document ID: 0990.37020
DOI: 10.1016/S0294-1449(98)80003-6
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2000-04-03T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78450
review text: The main goal of this paper is to show that in the unfolding of a three-dimensional vector field having a saddle-focus singular cycle hyperbolicity is a prevalent phenomenon: that is, the set of parameters corresponding to Axiom A flows has full Lebesgue density at this bifurcation value. Here for the first time nontrivial hyperbolicity is proved for the maximal invariant set for a perturbation of a vector field with a cycle containing a saddle-focus singularity.
Mathematics Subject Classification ID: 37C70
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 37D20
zbMATH DE Number: 1199911
zbMATH Keywords: unfolding
zbMATH Keywords: vector field
zbMATH Keywords: saddle-focus singular cycle
zbMATH Keywords: hyperbolicity
author: B. San Martín
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1199911