Poincaré-Hopf index and partial hyperbolicity
type: Item
instance of: scholarly article
title: Poincaré-Hopf index and partial hyperbolicity
zbMATH Open document ID: 1167.58022
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 2008-12-10T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/10076
review text: The author uses the theory of partially hyperbolic systems in order to find singularities of index 1 for vector fields with isolated zeroes in a 3-ball. The main result shows the existence of such singularities provided the maximal invariant set in the ball is partially hyperbolic, with volume expanding central subbundle, and the strong stable manifolds of the singularities are unknotted in the ball. Examples are given to motivate the hypotheses.
reviewed by: Maria Aparecida Soares Ruas
Mathematics Subject Classification ID: 58K45
Mathematics Subject Classification ID: 37C15
Mathematics Subject Classification ID: 37D30
zbMATH DE Number: 5380233
zbMATH Keywords: partially hyperbolic systems
zbMATH Keywords: index
zbMATH Keywords: stable manifolds
author: C. A. Morales
MaRDI profile type: Publication
OpenAlex ID: W2000329313
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DOI: 10.5802/AFST.1180
description: scientific article; zbMATH DE number 5380233