Differentiability and topology of labyrinths in the disc and annulus
type: Item
instance of: scholarly article
title: Differentiability and topology of labyrinths in the disc and annulus
zbMATH Open document ID: 0621.57013
DOI: 10.1016/0040-9383(87)90057-7
author: Gilbert Levitt
author: Harold Rosenberg
published in: Topology
publication date: 1987-01-01T00:00:00Z
review text: A foliation F of a surface M is called arational if F has no interior compact leaf, F is transverse to \(\delta\) M, and no separatrices join two singularities. Theorem: Let F be an arational foliation of the disc or annulus. If F is of class \(C^ 2\), then every regular leaf is compact. The authors also give a classification of arational foliations of a disc and of an annulus in the case when singularities are thorns and saddles with any number of prongs.
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 37C10
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 57N05
zbMATH DE Number: 4007264
zbMATH Keywords: foliation of an annulus
zbMATH Keywords: labyrinth
zbMATH Keywords: compact leaf
zbMATH Keywords: arational foliation of the disc
zbMATH Keywords: regular leaf
zbMATH Keywords: singularities
zbMATH Keywords: thorns
zbMATH Keywords: saddles
MaRDI profile type: Publication
full work available at URL: 0040-9383(87)90057-7
OpenAlex ID: W2033867301
description: scientific article; zbMATH DE number 4007264