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Polynomial extensions of van der Waerden’s and Szemerédi’s theorems

- V. Bergelson, A. Leibman
- Mathematics
- 1996

An extension of the classical van der Waerden and Szemeredi the- orems is proved for commuting operators whose exponents are polynomials. As a consequence, for example, one obtains the following… Expand

Multiple recurrence and nilsequences

- V. Bergelson, B. Host, Bryna Kra, I. Ruzsa
- Mathematics
- 1 March 2005

Aiming at a simultaneous extension of Khintchine’s and Furstenberg’s Recurrence theorems, we address the question if for a measure preserving system $(X,\mathcal{X},\mu,T)$ and a set… Expand

Weakly mixing PET

- V. Bergelson
- MathematicsErgodic Theory and Dynamical Systems
- 1 September 1987

Suppose that (X, ℬ, μ) is a probability measure space and T is an invertible measure perserving transformation of (X, ℬ, μ). T is called weakly mixing if for any two sets A1A2 ∈ ℬ one has:

Mixing actions of groups

- V. Bergelson, J. Rosenblatt
- Mathematics
- 1 March 1988

This special extreme is important for recurrence theorems and can be characterized in a number of interesting ways, see Furstenberg, Katznelson, and Ornstein [8]. This concept was extended to… Expand

Ergodic Ramsey Theory–an Update

- V. Bergelson
- Mathematics
- 1996

Our achievements on the theoretical front will be very poor indeed if...we close our eyes to problems and can only memorize isolated conclusions or principles... A mathematical discipline is alive… Expand

Distribution of values of bounded generalized polynomials

- V. Bergelson, A. Leibman
- Mathematics
- 6 June 2007

A generalized polynomial is a real-valued function which is obtained from conventional polynomials by the use of the operations of addition, multiplication, and taking the integer part; a generalized… Expand

AN INVERSE THEOREM FOR THE UNIFORMITY SEMINORMS ASSOCIATED WITH THE ACTION OF Fp

- V. Bergelson, T. Tao, T. Ziegler
- Mathematics
- 2010

Let F a finite field. We show that the universal characteristic factor for the Gowers–Host–Kra uniformity seminorm U(X) for an ergodic action (Tg)g∈Fω of the infinite abelian group F on a probability… Expand

Sumset phenomenon in countable amenable groups

- M. Beiglboeck, V. Bergelson, A. Fish
- Mathematics
- 14 May 2009

Partition Theorems for Spaces of Variable Words

- V. Bergelson, A. Blass, N. Hindman
- Mathematics
- 1 May 1994

Furstenberg and Katznelson applied methods of topological dynamics to Ramsey theory, obtaining a density version of the Hales-Jewett partition theorem. Inspired by their methods, but using spaces of… Expand

Multiplicative structures in additively large sets

- M. Beiglböck, V. Bergelson, N. Hindman, D. Strauss
- MathematicsJ. Comb. Theory, Ser. A
- 1 October 2006

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