Counterexamples to the Seifert conjecture
type: Item
instance of: scholarly article
title: Counterexamples to the Seifert conjecture
zbMATH Open document ID: 0924.58086
published in: Documenta Mathematica
publication date: 1998-08-06T00:00:00Z
full work available at URL: https://eudml.org/doc/222644
full work available at URL: Kuperberg.MAN.html
review text: Summary: Since H. Seifert proved in 1950 the existence of a periodic orbit for a vector field on the 3-dimensional sphere \(S^3\) which forms small angles with the fibers of the Hopf fibration, several examples of aperiodic vector fields on \(S^3\) have been produced as well as results showing that in some situations a compact orbit must exist. This paper surveys presently known types of vector fields without periodic orbits on \(S^3\) and on other manifolds.
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 37C85
zbMATH DE Number: 1184292
zbMATH Keywords: 3-dimensional sphere \(S^3\)
zbMATH Keywords: Hopf fibration
zbMATH Keywords: aperiodic vector fields on \(S^3\)
zbMATH Keywords: periodic orbits
zbMATH Keywords: dynamical system
zbMATH Keywords: plug
zbMATH Keywords: minimal set
zbMATH Keywords: PL foliation
author: Krystyna Kuperberg
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1184292