The set of vector fields with transverse foliations
type: Item
instance of: scholarly article
title: The set of vector fields with transverse foliations
zbMATH Open document ID: 0789.58062
author: Plácido Andrade
published in: Journal of the Mathematical Society of Japan
publication date: 1994-06-13T00:00:00Z
review text: Let \(M\) be a smooth three dimensional closed manifold and \(NSX(M)\) the space of \(C^ 1\) nonsingular vector fields on \(M\), endowed with the \(C^ 0\)-topology. By \(TF(M)\) is denoted the topological subspace of \(NSX(M)\) of vector fields whose flows admit a transverse foliation and by \(\overline{TF(M)}\) its closure. The author introduces the notion of homotopically linked flow. Then \(L(M)\) is the subset of \(NSX(M)\) consisting of vector fields whose flows are homotopically linked. The author proved among others that the sets \(TF(M)\) and \(L(M)\) are open and not dense in \(NSX(M)\), \(TF(M) \subset L(M) \subset \overline{TF(M)}\) and the \(TF(M)\) is invariant under topological conjugacy. This interesting paper is well written and organized.
Mathematics Subject Classification ID: 37C85
Mathematics Subject Classification ID: 37C10
zbMATH DE Number: 469048
zbMATH Keywords: chain recurrent set
zbMATH Keywords: filtration
zbMATH Keywords: transverse foliation
reviewed by: A. Klíč
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04510021
OpenAlex ID: W2063185821
DOI: 10.2969/JMSJ/04510021
description: scientific article; zbMATH DE number 469048