IPr⁎-recurrence and nilsystems

@article{Bergelson2018IPrrecurrenceAN,
  title={IPr⁎-recurrence and nilsystems},
  author={Vitaly Bergelson and Alexander Leibman},
  journal={Advances in Mathematics},
  year={2018}
}
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8 Citations

8 Citations

Polynomial orbits in totally minimal systems
Inspired by the recent work of Glasner, Huang, Shao, Weiss and Ye [13], we prove that the maximal ∞-step pro-nilfactor X∞ of a minimal system (X ,T ) is the topological characteristic factor along…
Multiplicative combinatorial properties of return time sets in minimal dynamical systems
We investigate the relationship between the dynamical properties of minimal topological dynamical systems and the multiplicative combinatorial properties of return time sets arising from those…
Ju l 2 02 1 Polynomial multiple recurrence and large intersections in rings of integers
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Simultaneous approximation in nilsystems and the multiplicative thickness of return-time sets
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Popular differences for polynomial patterns in rings of integers
We demonstrate that the phenomenon of popular differences (aka the phenomenon of large intersections) holds for natural families of polynomial patterns in rings of integers of number fields. If K is…
Bracket words: a generalisation of Sturmian words arising from generalised polynomials
Generalised polynomials are maps constructed by applying the floor function, addition, and multiplication to polynomials. Despite superficial similarity, generalised polynomials exhibit many…
Sublacunary sets and interpolation sets for nilsequences
  • A. Le
  • Computer Science
    Discrete & Continuous Dynamical Systems
  • 2021
TLDR
A new class of interpolation sets for Bohr almost periodic sequences is provided, and it is proved that the union of an interpolation set for nilsequences and a finite set is an interpolations set fornilsequences.
Sets of large values of correlation functions for polynomial cubic configurations
We prove that for any set $E\subseteq \mathbb{Z}$ with upper Banach density $d^{\ast }(E)>0$ , the set ‘of cubic configurations’ in $E$ is large in the following sense: for any $k\in \mathbb{N}$ and…

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