Volume 9, issue 3 (2005)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 20
Issue 4, 1807–2438
Issue 3, 1257–1806
Issue 2, 629–1255
Issue 1, 1–627

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Subscriptions
Author Index
To Appear
Contacts
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Structure des homeomorphismes de Brouwer

Frederic Le Roux

Geometry & Topology 9 (2005) 1689–1774

arXiv: math.DS/0403406

Abstract

For every Brouwer (ie planar, fixed point free, orientation preserving) homeomorphism h there exists a covering of the plane by translation domains, invariant simply-connected open subsets on which h is conjugate to an affine translation. We introduce a distance dh on the plane that counts the minimal number of translation domains connecting a pair of points. This allows us to describe a combinatorial conjugacy invariant, and to show the existence of a finite family of generalised Reeb components separating any two points x,y such that dh(x,y) > 1.

Résumé

Tout homéomorphisme de Brouwer s’obtient en recollant des domaines de translation (ouverts simplement connexes, invariants, en restriction auxquels la dynamique est conjuguée à une translation). On introduit une distance dh sur le plan qui compte le nombre minimal de domaines de translation dont la réunion connecte deux points. Ceci nous permet de décrire un invariant combinatoire de conjugaison, qui décrit très grossièrement la manière dont les domaines de translation se recollent. On montre également l’existence de structures dynamiques qui généralisent la présence de composantes de Reeb dans les feuilletages non triviaux du plan.

Keywords
homeomorphism, surface, fixed point, index, Reeb components, Brouwer
Mathematical Subject Classification 2000
Primary: 37E30
Secondary: 37B30
References
Forward citations
Publication
Received: 8 November 2004
Revised: 1 September 2005
Accepted: 18 August 2005
Published: 14 September 2005
Proposed: Benson Farb
Seconded: Leonid Polterovich, David Gabai
Authors
Frederic Le Roux
Université Paris Sud
Bat. 425
91405 Orsay Cedex
France