Volume 16, issue 4 (2012)

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

Volume 21
Issue 6, 3191–3810
Issue 5, 2557–3190
Issue 4, 1931–2555
Issue 3, 1285–1930
Issue 2, 647–1283
Issue 1, 1–645

Volume 20, 6 issues

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
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Entropy zero area preserving diffeomorphisms of $S^2$

John Franks and Michael Handel

Geometry & Topology 16 (2012) 2187–2284
Abstract

In this paper we formulate and prove a structure theorem for area preserving diffeomorphisms of genus zero surfaces with zero entropy and at least three periodic points. As one application we relate the existence of faithful actions of a finite index subgroup of the mapping class group of a closed surface Σg on S2 by area preserving diffeomorphisms to the existence of finite index subgroups of bounded mapping class groups MCG(S,S) with nontrivial first cohomology. In another application we show that the rotation number is defined and continuous at every point of a zero entropy area preserving diffeomorphism of the annulus.

Keywords
entropy zero diffeomorphism
Mathematical Subject Classification 2010
Primary: 37C05, 37C85
References
Publication
Received: 7 September 2010
Revised: 30 January 2012
Accepted: 25 July 2012
Published: 16 January 2013
Proposed: Danny Calegari
Seconded: Dmitri Burago, Leonid Polterovich
Authors
John Franks
Department of Mathematics
Northwestern University
Evanston, IL 60208-2730
United States
Michael Handel
Mathematics & Computer Science Department
Herbert H Lehman College
CUNY
Bronx, NY 10468-1589
United States