Bounded orbits and global fixed points for groups acting on the plane

Details Bounded orbits and global fixed points for groups acting on the plane Bounded orbits and global fixed points for groups acting on the plane

2011-03-25

arxiv.org/abs/1103.5060v1

Mathematics

Dynamical Systems

Scientific paper

Let G be a group acting on the plane by orientation-preserving homeomorphisms. We show that if for some k>0 there is a ball of radius r > k/\sqrt{3} such that each point x in the ball satisfies |gx -hx| < k for all g, h in G, and the action of G satisfies a nonwandering hypothesis, then the action has a global fixed point. In particular, any group of measure-preserving orientation preserving homeomorphisms of the plane with uniformly bounded orbits has a global fixed point. The constant k/\sqrt{3} is sharp. We also show that a group acting on the plane with orbits bounded as above is left orderable.

Affiliated with

Also associated with

No associations

Rating

Bounded orbits and global fixed points for groups acting on the plane does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Bounded orbits and global fixed points for groups acting on the plane, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bounded orbits and global fixed points for groups acting on the plane will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-571506