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

Tim Austin

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1667-1708
Number of pages42
JournalErgodic Theory and Dynamical Systems
Volume33
Issue number6
DOIs
StatePublished - Dec 2013

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Lie groups
Nilpotent Lie Group
Equidistribution
Joining
Polynomials
Polynomial
Subgroup
Ergodic Averages
Polynomial Maps
Recurrence
Trajectories
Trajectory
Norm
Invariant

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Equidistribution of joinings under off-diagonal polynomial flows of nilpotent Lie groups. / Austin, Tim.

In: Ergodic Theory and Dynamical Systems, Vol. 33, No. 6, 12.2013, p. 1667-1708.

Research output: Contribution to journalArticle

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