Entropy zero area preserving diffeomorphisms of $S^2$

Abstract

In this paper we formulate and prove a structure theorem for area preserving diffeomorphisms of genus zero surfaces with zero entropy. As an application we relate the existence of faithful actions of a finite index subgroup of the mapping class group of a closed surface ${\Sigma }_g$ on $S^2$ by area preserving diffeomorphisms to the existence of finite index subgroups of bounded mapping class groups $MCG(S,\partial S)$ with non-trivial first cohomology.

88 pages, 4 figures

References in corpus (1)

• Global fixed points for centralizers and Morita's Theorem

Cited by in corpus (4)

• Rotation intervals and entropy on attracting annular continua
• Global Rigidity of Some Abelian-by-Cyclic group actions on $\T^2$
• An index for Brouwer homeomorphisms and homotopy Brouwer theory
• On diffeomorphisms of compact 2-manifolds with all nonwandering points periodic