Multiple polynomial correlation sequences and nilsequences

DOI10.1017/S0143385709000303zbMath1205.37010OpenAlexW1989448167MaRDI QIDQ3569989

Alexander Leibman

Publication date: 22 June 2010

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

Full work available at URL: https://doi.org/10.1017/s0143385709000303

zbMATH Keywords

ergodicnilmanifoldsnilsequenceconvergence in uniform density

Mathematics Subject Classification ID

General groups of measure-preserving transformations (28D15) General groups of measure-preserving transformations and dynamical systems (37A15)

Related Items (19)

Some open problems on multiple ergodic averages ⋮ Linear sequences and weighted ergodic theorems ⋮ A decomposition of multicorrelation sequences for commuting transformations along primes ⋮ Single and multiple recurrence along non-polynomial sequences ⋮ Disjointness for measurably distal group actions and applications ⋮ Multiple correlation sequences and nilsequences ⋮ Nilsequences and multiple correlations along subsequences ⋮ Decomposition of multicorrelation sequences and joint ergodicity ⋮ Uniform distribution in nilmanifolds along functions from a Hardy field ⋮ Optimal lower bounds for multiple recurrence ⋮ Structure of multicorrelation sequences with integer part polynomial iterates along primes ⋮ Weighted multiple ergodic averages and correlation sequences ⋮ Integer part polynomial correlation sequences ⋮ Multiple ergodic averages for tempered functions ⋮ Nil Bohr\(_0\)-sets and polynomial recurrence ⋮ Nilsequences, null-sequences, and multiple correlation sequences ⋮ Properties of multicorrelation sequences and large returns under some ergodicity assumptions ⋮ Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics ⋮ A spectral refinement of the Bergelson–Host–Kra decomposition and new multiple ergodic theorems

Cites Work

• Unnamed Item
• Convergence of polynomial ergodic averages
• 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
• Universal characteristic factors and Furstenberg averages
• Orbits on a nilmanifold under the action of a polynomial sequence of translations
• Pointwise convergence of ergodic averages for polynomial sequences of translations on a nilmanifold
• Pointwise convergence of ergodic averages for polynomial actions of $\mathbb{Z}^{d}$ by translations on a nilmanifold
• Rational sub-nilmanifolds of a compact nilmanifold

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