On the Dynamics of G-Solenoids. Applications to Delone Sets

Details On the Dynamics of G-Solenoids. Applications to Delone Sets On the Dynamics of G-Solenoids. Applications to Delone Sets

2002-08-30

arxiv.org/abs/math/0208243v1

Mathematics

Dynamical Systems

26 pages

Scientific paper

A G-solenoid is a laminated space whose leaves are copies of a single Lie group G, and whose transversals are totally disconnected sets. It inherits a G-action and can be considered as dynamical system. Free Z^d-actions on the Cantor set as well as a large class of tiling spaces possess such a structure of G-solenoid. We show that a G-solenoid can be seen as a projective limit of branched manifolds modeled on G. This allows us to give a topological description of the transverse invariant measures associated with a G-solenoid in terms of a positive cone in the projective limit of the dim(G)-homology groups of these branched manifolds. In particular we exhibit a simple criterion implying unique ergodicity. A particular attention is paid to the case when the Lie group $G$ is the group of affine orientation preserving isometries of the Euclidean space or its subgroup of translations.

Affiliated with

Also associated with

No associations

Rating

On the Dynamics of G-Solenoids. Applications to Delone Sets 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 On the Dynamics of G-Solenoids. Applications to Delone Sets, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Dynamics of G-Solenoids. Applications to Delone Sets will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-252317