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Entropy zero area
preserving diffeomorphisms of $S^2$
John Franks and Michael Handel |
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Geometry & Topology 16 (2012) 2187–2284
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Abstract |
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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 on by area preserving diffeomorphisms to the existence of finite index subgroups of bounded mapping class groups 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
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Mathematical Subject Classification 2010
Primary: 37C05, 37C85
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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
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Authors |
| John Franks | |
| Department of Mathematics Northwestern University Evanston, IL 60208-2730 United States |
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| Michael Handel | |
| Mathematics & Computer Science
Department Herbert H Lehman College CUNY Bronx, NY 10468-1589 United States |
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