Physical Measure and Absolute Continuity for One-Dimensional Center Direction

Details Physical Measure and Absolute Continuity for One-Dimensional Center Direction Physical Measure and Absolute Continuity for One-Dimensional Center Direction

2010-12-02

arxiv.org/abs/1012.0513v1

Mathematics

Dynamical Systems

35 pages, 4 figures

Scientific paper

For a class of partially hyperbolic $C^k$, $k>1$ diffeomorphisms with circle center leaves we prove existence and finiteness of physical (or Sinai-Ruelle-Bowen) measures, whose basins cover a full Lebesgue measure subset of the ambient manifold. Our conditions contain an open and dense subset of all $C^k$ partially hyperbolic skew-products on compact circle bundles. Our arguments blend ideas from the theory of Gibbs states for diffeomorphisms with mostly contracting center direction together with recent progress in the theory of cocycles over hyperbolic systems that call into play geometric properties of invariant foliations such as absolute continuity. Recent results show that absolute continuity of the center foliation is often a rigid property among volume preserving systems. We prove that this is not at all the case in the dissipative setting, where absolute continuity can even be robust.

Affiliated with

Also associated with

No associations

Rating

Physical Measure and Absolute Continuity for One-Dimensional Center Direction 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 Physical Measure and Absolute Continuity for One-Dimensional Center Direction, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Physical Measure and Absolute Continuity for One-Dimensional Center Direction will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-604484