Pointwise convergence for cubic and polynomial multiple ergodic averages of non-commuting transformations

DOI10.1017/S014338571100006XzbMath1277.37018arXiv1006.5239MaRDI QIDQ2908163

Qing Chu, Nikos Frantzikinakis

Publication date: 4 September 2012

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.5239

zbMATH Keywords

pointwise convergencecharacteristic factorsmultiple ergodic averagesGowers-Host-Kra seminormscubical averagesshifted polynomial averages

Mathematics Subject Classification ID

Related Items (11)

Some open problems on multiple ergodic averages ⋮ Pointwise convergence of some multiple ergodic averages ⋮ Strictly ergodic models under face and parallelepiped group actions ⋮ Pointwise convergence of certain continuous-time double ergodic averages ⋮ Pointwise multiple averages for sublinear functions ⋮ Almost sure convergence of the multiple ergodic average for certain weakly mixing systems ⋮ Note on the continuity of the projection in the Host-Kra factors ⋮ A pointwise cubic average for two commuting transformations ⋮ Ergodicity of the Liouville system implies the Chowla conjecture ⋮ Pointwise convergence of multiple ergodic averages and strictly ergodic models ⋮ Multiple recurrence for non-commuting transformations along rationally independent polynomials

Cites Work

• Convergence of polynomial ergodic averages
• Pointwise convergence of ergodic averages along cubes
• Uniformity seminorms on \(\ell^{\infty}\) and applications
• Joint ergodicity and mixing
• Counterexamples in ergodic theory and number theory
• Multiple recurrence theorem for measure preserving actions of a nilpotent group
• Multiple recurrence and nilsequences (with an appendix by Imre Ruzsa)
• Convergence of multiple ergodic averages along polynomials of several variables
• Nonconventional ergodic averages and nilmanifolds
• Lower bounds for ergodic averages
• Weakly mixing PET
• Failure of the Roth theorem for solvable groups of exponential growth
• Pointwise convergence of ergodic averages for polynomial actions of $\mathbb{Z}^{d}$ by translations on a nilmanifold
• Polynomial extensions of van der Waerden’s and Szemerédi’s theorems
• A new proof of Szemerédi's theorem

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