Measure and cocycle rigidity for certain non-uniformly hyperbolic actions of higher rank abelian groups

Details Measure and cocycle rigidity for certain non-uniformly hyperbolic actions of higher rank abelian groups Measure and cocycle rigidity for certain non-uniformly hyperbolic actions of higher rank abelian groups

2010-01-14

arxiv.org/abs/1001.2473v1

Mathematics

Dynamical Systems

28 pages

Scientific paper

We prove absolute continuity of "high entropy" hyperbolic invariant measures for smooth actions of higher rank abelian groups assuming that there are no proportional Lyapunov exponents. For actions on tori and infranilmanifolds existence of an absolutely continuous invariant measure of this kind is obtained for actions whose elements are homotopic to those of an action by hyperbolic automorphisms with no multiple or proportional Lyapunov exponents. In the latter case a form of rigidity is proved for certain natural classes of cocycles over the action.

Affiliated with

Also associated with

No associations

Rating

Measure and cocycle rigidity for certain non-uniformly hyperbolic actions of higher rank abelian groups 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 Measure and cocycle rigidity for certain non-uniformly hyperbolic actions of higher rank abelian groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Measure and cocycle rigidity for certain non-uniformly hyperbolic actions of higher rank abelian groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-568329