Entropy zero area preserving diffeomorphisms of S2

John Franks*, Michael Handel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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
Issue number4
StatePublished - Jan 16 2013

ASJC Scopus subject areas

  • Geometry and Topology


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