## 8 Citations

Polynomial orbits in totally minimal systems

- Mathematics
- 2022

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

- MathematicsDiscrete & Continuous Dynamical Systems - A
- 2019

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

- Mathematics
- 2021

We establish characteristic factors for natural classes of polynomial multiple ergodic averages in rings of integers and derive corresponding Khintchine-type recurrence theorems, extending results of…

Simultaneous approximation in nilsystems and the multiplicative thickness of return-time sets

- Mathematics
- 2022

In the topological dynamical system (X,T ), a point x simultaneously approximates a point y if there exists a sequence n1, n2, . . . of natural numbers for which T ix, T ix, . . . , T ix all tend to…

Popular differences for polynomial patterns in rings of integers

- Mathematics
- 2021

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

- Mathematics
- 2022

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

- Computer ScienceDiscrete & Continuous Dynamical Systems
- 2021

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

- MathematicsErgodic Theory and Dynamical Systems
- 2016

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…

## References

SHOWING 1-10 OF 24 REFERENCES

Ultrafilters, IP sets, Dynamics, and Combinatorial Number Theory

- Mathematics
- 2010

We survey the connection between ultrafilters, ergodic theory, and combinatorics.

Infinite-step nilsystems, independence and complexity

- MathematicsErgodic Theory and Dynamical Systems
- 2011

Abstract An ∞-step nilsystem is an inverse limit of minimal nilsystems. In this article, it is shown that a minimal distal system is an ∞-step nilsystem if and only if it has no non-trivial pairs…

Nilsequences and a structure theorem for topological dynamical systems

- MathematicsAdvances in Mathematics
- 2010

Anzai and Furstenberg Transformations on the 2-Torus and Topologically Quasi-Discrete Spectrum

- MathematicsCanadian Mathematical Bulletin
- 1995

Abstract Let ϕ0 be an Anzai transformation on the 2-torus T2 defined by ϕ0(x,y) = (e2πiθx,xy) and ϕy a Furstenberg transformation on T2 defined by ϕf(x,y) = (e2πiθx,e2πif(x)xy) where θ is an…

Reflections on equicontinuity

- Mathematics
- 2011

We study different conditions which turn out to be equivalent to equicontinuity for a transitive compact Hausdorff flow with a general group action. Among them are a notion of "regional"…

Nonconventional ergodic averages and nilmanifolds

- Mathematics
- 2005

We study the L2-convergence of two types of ergodic averages. The first is the average of a product of functions evaluated at return times along arithmetic progressions, such as the expressions…

Some counterexamples in topological dynamics

- MathematicsErgodic Theory and Dynamical Systems
- 2008

Abstract In this paper, we exhibit, for any sparse-enough increasing sequence {pn} of integers, totally minimal, totally uniquely ergodic, and topologically mixing systems (X,T) and (X′,T′) and…

The Mobius function is strongly orthogonal to nilsequences

- Mathematics
- 2008

We show that the Mobius function (n) is strongly asymptotically or- thogonal to any polynomial nilsequence (F (g(n))) n2N. Here, G is a sim- ply-connected nilpotent Lie group with a discrete and…

A study of the proximal relation in coset transformation groups

- Mathematics
- 1967

1. Introduction. In this paper, we investigate the proximal relation and related notions in coset transformation groups. In ?1, we show that many of the interesting properties of the proximal…

Nil Bohr-sets and almost automorphy of higher order

- Mathematics
- 2014

Two closely related topics: higher order Bohr sets and higher order almost automorphy are investigated in this paper. Both of them are related to nilsystems.
In the first part, the problem which can…