Equidistribution of joinings under off-diagonal polynomial flows of nilpotent Lie groups

Details Equidistribution of joinings under off-diagonal polynomial flows of nilpotent Lie groups Equidistribution of joinings under off-diagonal polynomial flows of nilpotent Lie groups

2011-05-27

arxiv.org/abs/1105.5612v4

Mathematics

Dynamical Systems

57 pages [TDA Sep 27th, 2011:] Several minor improvements made and some references added [TDA Feb 1st, 2012:] A few more minor

Scientific paper

Let $G$ be a connected nilpotent Lie group. Given probability-preserving $G$-actions $(X_i,\S_i,\mu_i,u_i)$, $i=0,1,...,k$, and also polynomial maps $\phi_i:\bbR\to G$, $i=1,...,k$, we consider the trajectory of a joining $\l$ of the systems $(X_i,\S_i,\mu_i,u_i)$ under the `off-diagonal' flow [(t,(x_0,x_1,x_2,...,x_k))\mapsto (x_0,u_1^{\phi_1(t)}x_1,u_2^{\phi_2(t)}x_2,...,u_k^{\phi_k(t)}x_k).] It is proved that any joining $\l$ is equidistributed under this flow with respect to some limit joining $\l'$. This is deduced from the stronger fact of norm convergence for a system of multiple ergodic averages, related to those arising in Furstenberg's approach to the study of multiple recurrence. It is also shown that the limit joining $\l'$ is invariant under the subgroup of $G^{k+1}$ generated by the image of the off-diagonal flow, in addition to the diagonal subgroup.

Affiliated with

Also associated with

No associations

Rating

Equidistribution of joinings under off-diagonal polynomial flows of nilpotent Lie 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 Equidistribution of joinings under off-diagonal polynomial flows of nilpotent Lie groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Equidistribution of joinings under off-diagonal polynomial flows of nilpotent Lie groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-666078