Multiple recurrence and convergence results associated to FPω-actions

Vitaly Bergelson; Terence Tao; Tamar Ziegler

doi:10.1007/s11854-015-0033-1

Multiple recurrence and convergence results associated to F_P^ω-actions

Vitaly Bergelson^*, Terence Tao, Tamar Ziegler

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Using an ergodic inverse theorem obtained in our previous paper, we obtain limit formulae for multiple ergodic averages associated with the action of (Formula Presented.). From this we deduce multiple Khintchine-type recurrence results analogous to those for ℤ-systems obtained by Bergelson, Host, and Kra, and also present some new counterexamples in this setting.

Original language	American English
Pages (from-to)	329-378
Number of pages	50
Journal	Journal d'Analyse Mathematique
Volume	127
Issue number	1
DOIs	https://doi.org/10.1007/s11854-015-0033-1
State	Published - 1 Sep 2015
Externally published	Yes

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Publisher Copyright:
© 2015, Hebrew University Magnes Press.

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10.1007/s11854-015-0033-1

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title = "Multiple recurrence and convergence results associated to FPω-actions",

abstract = "Using an ergodic inverse theorem obtained in our previous paper, we obtain limit formulae for multiple ergodic averages associated with the action of (Formula Presented.). From this we deduce multiple Khintchine-type recurrence results analogous to those for ℤ-systems obtained by Bergelson, Host, and Kra, and also present some new counterexamples in this setting.",

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T1 - Multiple recurrence and convergence results associated to FPω-actions

AU - Bergelson, Vitaly

AU - Tao, Terence

AU - Ziegler, Tamar

PY - 2015/9/1

Y1 - 2015/9/1

N2 - Using an ergodic inverse theorem obtained in our previous paper, we obtain limit formulae for multiple ergodic averages associated with the action of (Formula Presented.). From this we deduce multiple Khintchine-type recurrence results analogous to those for ℤ-systems obtained by Bergelson, Host, and Kra, and also present some new counterexamples in this setting.

AB - Using an ergodic inverse theorem obtained in our previous paper, we obtain limit formulae for multiple ergodic averages associated with the action of (Formula Presented.). From this we deduce multiple Khintchine-type recurrence results analogous to those for ℤ-systems obtained by Bergelson, Host, and Kra, and also present some new counterexamples in this setting.

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U2 - 10.1007/s11854-015-0033-1

DO - 10.1007/s11854-015-0033-1

M3 - Article

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VL - 127

SP - 329

EP - 378

JO - Journal d'Analyse Mathematique

JF - Journal d'Analyse Mathematique

IS - 1

ER -

Multiple recurrence and convergence results associated to F_P^ω-actions

Abstract

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