Fixed Points of abelian actions on $S^2$

Details Fixed Points of abelian actions on $S^2$ Fixed Points of abelian actions on $S^2$

2005-09-23

arxiv.org/abs/math/0509574v2

Mathematics

Dynamical Systems

Scientific paper

We prove that if $F$ is a finitely generated abelian group of orientation preserving $C^1$ diffeomorphisms of $R^2$ which leaves invariant a compact set then there is a common fixed point for all elements of $F.$ We also show that if $F$ is any abelian subgroup of orientation preserving $C^1$ diffeomorphisms of $S^2$ then there is a common fixed point for all elements of a subgroup of $F$ with index at most two.

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