Entropy zero area preserving diffeomorphisms of S2

John M Franks, Michael Handel

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 ∑g 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.

Original languageEnglish (US)
Pages (from-to)2187-2284
Number of pages98
JournalGeometry and Topology
Volume16
Issue number4
DOIs
StatePublished - Jan 16 2013

Fingerprint

Diffeomorphisms
Mapping Class Group
Entropy
Zero
Subgroup
Rotation number
Structure Theorem
Periodic Points
Diffeomorphism
Ring or annulus
Faithful
Cohomology
Genus
Closed

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Franks, John M ; Handel, Michael. / Entropy zero area preserving diffeomorphisms of S2. In: Geometry and Topology. 2013 ; Vol. 16, No. 4. pp. 2187-2284.
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Entropy zero area preserving diffeomorphisms of S2. / Franks, John M; Handel, Michael.

In: Geometry and Topology, Vol. 16, No. 4, 16.01.2013, p. 2187-2284.

Research output: Contribution to journalArticle

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