Convergence of polynomial ergodic averages of several variables for some commuting transformations

zbMath1210.28017arXiv0906.3266MaRDI QIDQ610628

Michael C. R. Johnson

Publication date: 8 December 2010

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.3266

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) General groups of measure-preserving transformations and dynamical systems (37A15)

Related Items (5)

Some open problems on multiple ergodic averages ⋮ Seminorms for multiple averages along polynomials and applications to joint ergodicity ⋮ Decomposition of multicorrelation sequences and joint ergodicity ⋮ Properties of multicorrelation sequences and large returns under some ergodicity assumptions ⋮ Poincaré recurrence and number theory: thirty years later

Cites Work

• Convergence of polynomial ergodic averages
• Ergodic behavior of diagonal measures and a theorem of Szemeredi on arithmetic progressions
• Convergence of multiple ergodic averages along polynomials of several variables
• Nonconventional ergodic averages and nilmanifolds
• The ergodic theorem
• Weakly mixing PET
• A Roth theorem for amenable groups.
• Pointwise convergence of ergodic averages for polynomial actions of $\mathbb{Z}^{d}$ by translations on a nilmanifold
• Norm convergence of multiple ergodic averages for commuting transformations
• Convergence of multiple ergodic averages for some commuting transformations
• Polynomial extensions of van der Waerden’s and Szemerédi’s theorems

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