TY - JOUR

T1 - Equidistribution of joinings under off-diagonal polynomial flows of nilpotent Lie groups

AU - Austin, Tim

N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

PY - 2013/12

Y1 - 2013/12

N2 - Let G be a connected nilpotent Lie group. Given probability-preserving G-actions (Xi ; Σi ; μi ; μi), i = 0, 1;..., k, and also polynomial maps 'i V ℝ → G, i = 1, ... , k, we consider the trajectory of a joining λ of the systems (Xi ; Σi ; μi ; μi) under the 'off-diagonal' flow (eqution presented) It is proved that any joining is equidistributed under this flow with respect to some limit joining λ0. 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 λ0 is invariant under the subgroup of GkC1 generated by the image of the off-diagonal flow, in addition to the diagonal subgroup.

AB - Let G be a connected nilpotent Lie group. Given probability-preserving G-actions (Xi ; Σi ; μi ; μi), i = 0, 1;..., k, and also polynomial maps 'i V ℝ → G, i = 1, ... , k, we consider the trajectory of a joining λ of the systems (Xi ; Σi ; μi ; μi) under the 'off-diagonal' flow (eqution presented) It is proved that any joining is equidistributed under this flow with respect to some limit joining λ0. 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 λ0 is invariant under the subgroup of GkC1 generated by the image of the off-diagonal flow, in addition to the diagonal subgroup.

UR - http://www.scopus.com/inward/record.url?scp=84893116570&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893116570&partnerID=8YFLogxK

U2 - 10.1017/etds.2012.113

DO - 10.1017/etds.2012.113

M3 - Article

AN - SCOPUS:84893116570

VL - 33

SP - 1667

EP - 1708

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

SN - 0143-3857

IS - 6

ER -