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Bergelson, Vitaly

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Author ID: bergelson.vitaly Recent zbMATH articles by "Bergelson, Vitaly"
Published as: Bergelson, V.; Bergelson, Vitaly
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Documents Indexed: 124 Publications since 1984, including 3 Books

Publications by Year

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114 Publications have been cited 1,230 times in 542 Documents Cited by Year
Polynomial extensions of van der Waerden’s and Szemerédi’s theorems. Zbl 0870.11015
Bergelson, V.; Leibman, A.
109
1996
Multiple recurrence and nilsequences (with an appendix by Imre Ruzsa). Zbl 1087.28007
Bergelson, Vitaly; Host, Bernard; Kra, Bryna
66
2005
Weakly mixing PET. Zbl 0645.28012
Bergelson, V.
62
1987
Ergodic Ramsey theory – an update. Zbl 0846.05095
Bergelson, Vitaly
45
1996
Nonmetrizable topological dynamics and Ramsey theory. Zbl 0725.22001
Bergelson, Vitaly; Hindman, Neil
45
1990
Distribution of values of bounded generalized polynomials. Zbl 1137.37005
Bergelson, Vitaly; Leibman, Alexander
33
2007
Minimal idempotents and ergodic Ramsey theory. Zbl 1039.05063
Bergelson, Vitaly
27
2003
An ergodic IP polynomial Szemerédi theorem. Zbl 0948.28010
Bergelson, Vitaly; McCutcheon, Randall
27
2000
Set-polynomials and polynomial extension of the Hales-Jewett theorem. Zbl 0969.05061
Bergelson, V.; Leibman, A.
24
1999
Notions of size and combinatorial properties of quotient sets in semigroups. Zbl 0946.22002
Bergelson, Vitaly; Hindman, Neil; McCutcheon, Randall
23
1998
Partition theorems for spaces of variable words. Zbl 0809.04005
Bergelson, Vitaly; Blass, Andreas; Hindman, Neil
23
1994
Ultrafilters, IP sets, dynamics, and combinatorial number theory. Zbl 1237.05205
Bergelson, Vitaly
21
2010
Large sets of integers and hierarchy of mixing properties of measure preserving systems. Zbl 1142.37003
Bergelson, Vitaly; Downarowicz, Tomasz
21
2008
Intersective polynomials and the polynomial Szemerédi theorem. Zbl 1156.11007
Bergelson, V.; Leibman, A.; Lesigne, E.
20
2008
IP-sets and polynomial recurrence. Zbl 0958.28013
Bergelson, Vitaly; Furstenberg, Hillel; McCutcheon, Randall
20
1996
Weak mixing implies weak mixing of higher orders along tempered functions. Zbl 1184.37009
Bergelson, Vitaly; Knutson Håland, Inger J.
19
2009
Multiplicative structures in additively large sets. Zbl 1105.05071
Beiglböck, Mathias; Bergelson, Vitaly; Hindman, Neil; Strauss, Dona
19
2006
Partition regular structures contained in large sets are abundant. Zbl 0966.05078
Bergelson, Vitaly; Hindman, Neil
19
2001
Sumset phenomenon in countable amenable groups. Zbl 1187.43002
Beiglböck, Mathias; Bergelson, Vitaly; Fish, Alexander
18
2010
Piecewise-Bohr sets of integers and combinatorial number theory. Zbl 1114.37008
Bergelson, Vitaly; Furstenberg, Hillel; Weiss, Benjamin
17
2006
A Roth theorem for amenable groups. Zbl 0886.43002
Bergelson, Vitaly; McCutcheon, Randall; Zhang, Qing
17
1997
Sets of recurrence of \(\mathbb Z^m\)-actions and properties of sets of differences in \(\mathbb Z^m\). Zbl 0579.10029
Bergelson, Vitaly
17
1985
Rigidity and non-recurrence along sequences. Zbl 1351.37002
Bergelson, V.; Del Junco, A.; Lemańczyk, M.; Rosenblatt, J.
15
2014
An inverse theorem for the uniformity seminorms associated with the action of \(\mathbb F_p^\infty\). Zbl 1189.37007
Bergelson, Vitaly; Tao, Terence; Ziegler, Tamar
15
2010
Central sets and a non-commutative Roth theorem. Zbl 1201.37003
Bergelson, V.; McCutcheon, R.
15
2007
Mixing actions of groups. Zbl 0619.43005
Bergelson, Vitaly; Rosenblatt, Joseph
15
1988
Combinatorial and Diophantine applications of ergodic theory. (With Appendix A by A. Leibman, with Appendix B by Anthony Quas and Máté Wierdl). Zbl 1130.37317
Bergelson, Vitaly
14
2006
A nilpotent Roth theorem. Zbl 1042.37001
Bergelson, V.; Leibman, A.
14
2002
Recurrence for semigroup actions and a non-commutative Schur theorem. Zbl 0905.28010
Bergelson, V.; McCutcheon, R.
13
1998
Idempotent ultrafilters, multipleweak mixing and Szemerédi’s theorem for generalized polynomials. Zbl 1220.37003
Bergelson, Vitaly; McCutcheon, Randall
12
2010
Aspects of uniformity in recurrence. Zbl 0966.28009
Bergelson, Vitaly; Host, Bernard; McCutcheon, Randall; Parreau, François
12
2000
From discrete- to continuous-time ergodic theorems. Zbl 1251.37004
Bergelson, V.; Leibman, A.; Moreira, C. G.
11
2012
On \(\text{IP}^*\) sets and central sets. Zbl 0820.05061
Bergelson, Vitaly; Hindman, Neil
11
1994
Some results on nonlinear recurrence. Zbl 0803.28011
Bergelson, V.; Boshernitzan, M.; Bourgain, J.
11
1994
Ergodic Ramsey theory. Zbl 0642.10052
Bergelson, Vitaly
11
1987
The shifted primes and the multidimensional Szemerédi and polynomial Van der Waerden theorems. Zbl 1230.11017
Bergelson, Vitaly; Leibman, Alexander; Ziegler, Tamar
10
2011
Van der Corput sets in \(\mathbb Z^d\). Zbl 1177.37018
Bergelson, Vitaly; Lesigne, Emmanuel
10
2008
Multiplicatively large sets and ergodic Ramsey theory. Zbl 1093.11003
Bergelson, Vitaly
10
2005
Ergodic theory and diophantine problems. Zbl 0972.37008
Bergelson, Vitaly
10
2000
Multiplicative subgroups of finite index in a ring. Zbl 0784.12002
Bergelson, Vitaly; Shapiro, Daniel B.
10
1992
A density statement generalizing Schur’s theorem. Zbl 0607.10040
Bergelson, Vitaly
10
1986
IP-systems, generalized polynomials and recurrence. Zbl 1107.37007
Bergelson, Vitaly; Knutson, Inger J.; McCutcheon, Randall
9
2006
Polynomial Szemerédi theorems for countable modules over integral domains and finite fields. Zbl 1087.11007
Bergelson, V.; Leibman, A.; McCutcheon, R.
9
2005
Solvability of Rado systems in \(D\)-sets. Zbl 1231.05269
Beiglböck, M.; Bergelson, V.; Downarowicz, T.; Fish, A.
8
2009
The multifarious Poincaré recurrence theorem. Zbl 0957.05105
Bergelson, Vitaly
8
2000
Sets of recurrence and generalized polynomials. Zbl 0958.28014
Bergelson, Vitaly; Håland, Inger Johanne
8
1996
A combinatorially large cell of a partition of N. Zbl 0642.05003
Bergelson, Vitaly; Hindman, Neil
8
1988
Jointly ergodic measure-preserving transformations. Zbl 0571.28012
Berend, Daniel; Bergelson, Vitaly
8
1984
Multiple recurrence in quasirandom groups. Zbl 1336.37007
Bergelson, Vitaly; Tao, Terence
7
2014
Some new results in multiplicative and additive Ramsey theory. Zbl 1136.05074
Beiglböck, Mathias; Bergelson, Vitaly; Hindman, Neil; Strauss, Dona
7
2008
Uniformity in the polynomial Szemerédi theorem. Zbl 0862.28014
Bergelson, Vitaly; McCutcheon, Randall
7
1996
Additive and multiplicative Ramsey theorems in \(\mathbb{N}\)—some elementary results. Zbl 0794.05127
Bergelson, Vitaly; Hindman, Neil
7
1993
Ramsey theory in noncommutative semigroups. Zbl 0757.05009
Bergelson, Vitaly; Hindman, Neil
7
1992
Some topological semicommutative van der Waerden type theorems and their combinatorial consequences. Zbl 0761.05008
Bergelson, Vitaly; Hindman, Neil
7
1992
Ergodic and mixing sequences of transformations. Zbl 0536.28008
Berend, Daniel; Bergelson, Vitaly
7
1984
Ergodic theorem involving additive and multiplicative groups of a field and \(\{x+y,xy\}\) patterns. Zbl 1367.37002
Bergelson, Vitaly; Moreira, Joel
6
2017
Uniform distribution of prime powers and sets of recurrence and van der Corput sets in \(\mathbb{Z}^k\). Zbl 1316.11062
Bergelson, Vitaly; Kolesnik, Grigori; Madritsch, Manfred; Son, Younghwan; Tichy, Robert
6
2014
Strongly central sets and sets of polynomial returns mod 1. Zbl 1270.05097
Bergelson, Vitaly; Hindman, Neil; Strauss, Dona
6
2012
Complexities of finite families of polynomials, Weyl systems, and constructions in combinatorial number theory. Zbl 1146.37007
Bergelson, V.; Leibman, A.; Lesigne, E.
6
2007
Failure of the Roth theorem for solvable groups of exponential growth. Zbl 1115.37003
Bergelson, V.; Leibman, A.
6
2004
Topological multiple recurrence for polynomial configurations in nilpotent groups. Zbl 1016.05070
Bergelson, V.; Leibman, A.
6
2003
Additive and multiplicative Ramsey theory in the reals and the rationals. Zbl 0917.05080
Bergelson, Vitaly; Hindman, Neil; Leader, Imre
6
1999
Ultrafilters and multidimensional Ramsey theorems. Zbl 0693.05007
Bergelson, V.; Hindman, N.
6
1989
Uniform distribution of subpolynomial functions along primes and applications. Zbl 07074785
Bergelson, Vitaly; Kolesnik, Grigori; Son, Younghwan
5
2019
Polynomial recurrence with large intersection over countable fields. Zbl 1365.37009
Bergelson, Vitaly; Robertson, Donald
5
2016
Simultaneous dense and nondense orbits for commuting maps. Zbl 1352.37124
Bergelson, Vitaly; Einsiedler, Manfred; Tseng, Jimmy
5
2015
WM groups and Ramsey theory. Zbl 1231.05270
Bergelson, Vitaly; Furstenberg, Hillel
5
2009
Ledrappier’s system is almost mixing of all orders. Zbl 1154.37300
Arenas-Carmona, L.; Berend, D.; Bergelson, V.
5
2008
Affine actions of a free semigroup on the real line. Zbl 1143.37006
Bergelson, Vitaly; Misiurewicz, Michał; Senti, Samuel
5
2006
Weakly mixing group actions: a brief survey and an example. Zbl 1161.37006
Bergelson, V.; Gorodnik, A.
5
2004
Iterated spectra of numbers—elementary, dynamical, and algebraic approaches. Zbl 0855.05098
Bergelson, Vitaly; Hindman, Neil; Kra, Bryna
5
1996
Rado’s theorem for finite fields. Zbl 0838.05009
Bergelson, V.; Deuber, W. A.; Hindman, N.
5
1992
Density versions of two generalizations of Schur’s theorem. Zbl 0642.05002
Bergelson, Vitaly; Hindman, Neil
5
1988
Characterization of joint ergodicity for non-commuting transformations. Zbl 0619.28012
Berend, Daniel; Bergelson, Vitaly
5
1986
Multiplicative richness of additively large sets in \(\mathbb{Z}^d\). Zbl 1404.05209
Bergelson, Vitaly; Glasscock, Daniel
4
2018
Sets of large values of correlation functions for polynomial cubic configurations. Zbl 1388.37007
Bergelson, V.; Leibman, A.
4
2018
Measure preserving actions of affine semigroups and \(\{x+y,xy\}\) patterns. Zbl 1427.37001
Bergelson, Vitaly; Moreira, Joel
4
2018
Quotient sets and density recurrent sets. Zbl 1273.22002
Bergelson, Vitaly; Hindman, Neil
4
2012
A selection of open problems. Zbl 1217.05223
Bergelson, Vitaly (ed.); Rothschild, Bruce (ed.)
4
2009
Ergodicity and mixing of non-commuting epimorphisms. Zbl 1127.37007
Bergelson, Vitaly; Gorodnik, Alexander
4
2007
Squarefree numbers, IP sets and ergodic theory. Zbl 1042.11006
Bergelson, V.; Ruzsa, I.
4
2002
Rado’s theorem for commutative rings. Zbl 0795.05140
Bergelson, Vitaly; Deuber, Walter; Hindman, Neil; Lefmann, Hanno
4
1994
An algebraic proof of van der Waerden’s theorem. Zbl 0704.22004
Bergelson, Vitaly; Furstenberg, Hillel; Hindman, Neil; Katznelson, Yitzhak
4
1989
Mixing sequences in Hilbert spaces. Zbl 0611.47021
Berend, Daniel; Bergelson, Vitaly
4
1986
On the interplay between additive and multiplicative largeness and its combinatorial applications. Zbl 1433.05313
Bergelson, Vitaly; Glasscock, Daniel
3
2020
\(\mathrm{IP}_r^\ast\)-recurrence and nilsystems. Zbl 1444.37012
Bergelson, V.; Leibman, A.
3
2018
New examples of complete sets, with connections to a Diophantine theorem of Furstenberg. Zbl 1435.11021
Bergelson, Vitaly; Simmons, David
3
2017
New polynomial and multidimensional extensions of classical partition results. Zbl 1352.05023
Bergelson, Vitaly; Johnson, John H. jun.; Moreira, Joel
3
2017
Joint ergodicity along generalized linear functions. Zbl 1370.37006
Bergelson, V.; Leibman, A.; Son, Y.
3
2016
Van der Corput’s difference theorem: some modern developments. Zbl 1353.37011
Bergelson, Vitaly; Moreira, Joel
3
2016
Cubic averages and large intersections. Zbl 1336.28012
Bergelson, V.; Leibman, A.
3
2015
Simultaneous Diophantine approximation and VIP systems. Zbl 1142.11048
Bergelson, Vitaly; Håland Knutson, Inger J.; McCutcheon, Randall
3
2005
Sets partition regular for \(n\) equations need not solve \(n+1\). Zbl 0859.04001
Bergelson, Vitaly; Hindman, Neil; Leader, Imre
3
1996
Convergence in ergodic theory and probability. Papers from the conference, Ohio State University, Columbus, OH, USA, June 23–26, 1993. Zbl 0846.00030
Bergelson, V. (ed.); March, P. (ed.); Rosenblatt, J. (ed.)
3
1996
Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics. Zbl 1422.37008
Bergelson, V.; Kułaga-Przymus, J.; Lemańczyk, M.; Richter, F. K.
2
2019
Triangles in Cartesian squares of quasirandom groups. Zbl 1371.05314
Bergelson, V.; Robertson, D.; Zorin-Kranich, P.
2
2017
Polynomial multiple recurrence over rings of integers. Zbl 1373.37021
Bergelson, Vitaly; Robertson, Donald
2
2016
Finite products sets and minimally almost periodic groups. Zbl 1358.37009
Bergelson, V.; Christopherson, J. C.; Robertson, D.; Zorin-Kranich, P.
2
2016
Multiple recurrence and convergence results associated to \(\mathbb F_P^\omega\)-actions. Zbl 1361.37006
Bergelson, Vitaly; Tao, Terence; Ziegler, Tamar
2
2015
Polynomial extensions of the Milliken-Taylor theorem. Zbl 1359.03036
Bergelson, Vitaly; Hindman, Neil; Williams, Kendall
2
2014
On the interplay between additive and multiplicative largeness and its combinatorial applications. Zbl 1433.05313
Bergelson, Vitaly; Glasscock, Daniel
3
2020
Single and multiple recurrence along non-polynomial sequences. Zbl 1441.37004
Bergelson, Vitaly; Moreira, Joel; Richter, Florian K.
1
2020
A structure theorem for level sets of multiplicative functions and applications. Zbl 1447.37009
Bergelson, Vitaly; Kułaga-Przymus, Joanna; Lemańczyk, Mariusz; Richter, Florian K.
1
2020
Uniform distribution of subpolynomial functions along primes and applications. Zbl 07074785
Bergelson, Vitaly; Kolesnik, Grigori; Son, Younghwan
5
2019
Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics. Zbl 1422.37008
Bergelson, V.; Kułaga-Przymus, J.; Lemańczyk, M.; Richter, F. K.
2
2019
Multiplicative richness of additively large sets in \(\mathbb{Z}^d\). Zbl 1404.05209
Bergelson, Vitaly; Glasscock, Daniel
4
2018
Sets of large values of correlation functions for polynomial cubic configurations. Zbl 1388.37007
Bergelson, V.; Leibman, A.
4
2018
Measure preserving actions of affine semigroups and \(\{x+y,xy\}\) patterns. Zbl 1427.37001
Bergelson, Vitaly; Moreira, Joel
4
2018
\(\mathrm{IP}_r^\ast\)-recurrence and nilsystems. Zbl 1444.37012
Bergelson, V.; Leibman, A.
3
2018
Ergodic theorem involving additive and multiplicative groups of a field and \(\{x+y,xy\}\) patterns. Zbl 1367.37002
Bergelson, Vitaly; Moreira, Joel
6
2017
New examples of complete sets, with connections to a Diophantine theorem of Furstenberg. Zbl 1435.11021
Bergelson, Vitaly; Simmons, David
3
2017
New polynomial and multidimensional extensions of classical partition results. Zbl 1352.05023
Bergelson, Vitaly; Johnson, John H. jun.; Moreira, Joel
3
2017
Triangles in Cartesian squares of quasirandom groups. Zbl 1371.05314
Bergelson, V.; Robertson, D.; Zorin-Kranich, P.
2
2017
Polynomial recurrence with large intersection over countable fields. Zbl 1365.37009
Bergelson, Vitaly; Robertson, Donald
5
2016
Joint ergodicity along generalized linear functions. Zbl 1370.37006
Bergelson, V.; Leibman, A.; Son, Y.
3
2016
Van der Corput’s difference theorem: some modern developments. Zbl 1353.37011
Bergelson, Vitaly; Moreira, Joel
3
2016
Polynomial multiple recurrence over rings of integers. Zbl 1373.37021
Bergelson, Vitaly; Robertson, Donald
2
2016
Finite products sets and minimally almost periodic groups. Zbl 1358.37009
Bergelson, V.; Christopherson, J. C.; Robertson, D.; Zorin-Kranich, P.
2
2016
A Weyl-type equidistribution theorem in finite characteristic. Zbl 1336.37003
Bergelson, V.; Leibman, A.
1
2016
Simultaneous dense and nondense orbits for commuting maps. Zbl 1352.37124
Bergelson, Vitaly; Einsiedler, Manfred; Tseng, Jimmy
5
2015
Cubic averages and large intersections. Zbl 1336.28012
Bergelson, V.; Leibman, A.
3
2015
Multiple recurrence and convergence results associated to \(\mathbb F_P^\omega\)-actions. Zbl 1361.37006
Bergelson, Vitaly; Tao, Terence; Ziegler, Tamar
2
2015
Rigidity and non-recurrence along sequences. Zbl 1351.37002
Bergelson, V.; Del Junco, A.; Lemańczyk, M.; Rosenblatt, J.
15
2014
Multiple recurrence in quasirandom groups. Zbl 1336.37007
Bergelson, Vitaly; Tao, Terence
7
2014
Uniform distribution of prime powers and sets of recurrence and van der Corput sets in \(\mathbb{Z}^k\). Zbl 1316.11062
Bergelson, Vitaly; Kolesnik, Grigori; Madritsch, Manfred; Son, Younghwan; Tichy, Robert
6
2014
Polynomial extensions of the Milliken-Taylor theorem. Zbl 1359.03036
Bergelson, Vitaly; Hindman, Neil; Williams, Kendall
2
2014
From discrete- to continuous-time ergodic theorems. Zbl 1251.37004
Bergelson, V.; Leibman, A.; Moreira, C. G.
11
2012
Strongly central sets and sets of polynomial returns mod 1. Zbl 1270.05097
Bergelson, Vitaly; Hindman, Neil; Strauss, Dona
6
2012
Quotient sets and density recurrent sets. Zbl 1273.22002
Bergelson, Vitaly; Hindman, Neil
4
2012
The shifted primes and the multidimensional Szemerédi and polynomial Van der Waerden theorems. Zbl 1230.11017
Bergelson, Vitaly; Leibman, Alexander; Ziegler, Tamar
10
2011
Polynomials at iterated spectra near zero. Zbl 1226.05246
Bergelson, Vitaly; Hindman, Neil; Strauss, Dona
1
2011
Ultrafilters, IP sets, dynamics, and combinatorial number theory. Zbl 1237.05205
Bergelson, Vitaly
21
2010
Sumset phenomenon in countable amenable groups. Zbl 1187.43002
Beiglböck, Mathias; Bergelson, Vitaly; Fish, Alexander
18
2010
An inverse theorem for the uniformity seminorms associated with the action of \(\mathbb F_p^\infty\). Zbl 1189.37007
Bergelson, Vitaly; Tao, Terence; Ziegler, Tamar
15
2010
Idempotent ultrafilters, multipleweak mixing and Szemerédi’s theorem for generalized polynomials. Zbl 1220.37003
Bergelson, Vitaly; McCutcheon, Randall
12
2010
Weak mixing implies weak mixing of higher orders along tempered functions. Zbl 1184.37009
Bergelson, Vitaly; Knutson Håland, Inger J.
19
2009
Solvability of Rado systems in \(D\)-sets. Zbl 1231.05269
Beiglböck, M.; Bergelson, V.; Downarowicz, T.; Fish, A.
8
2009
WM groups and Ramsey theory. Zbl 1231.05270
Bergelson, Vitaly; Furstenberg, Hillel
5
2009
A selection of open problems. Zbl 1217.05223
Bergelson, Vitaly (ed.); Rothschild, Bruce (ed.)
4
2009
Sumsets in difference sets. Zbl 1250.11009
Bergelson, Vitaly; Ruzsa, Imre Z.
1
2009
Large sets of integers and hierarchy of mixing properties of measure preserving systems. Zbl 1142.37003
Bergelson, Vitaly; Downarowicz, Tomasz
21
2008
Intersective polynomials and the polynomial Szemerédi theorem. Zbl 1156.11007
Bergelson, V.; Leibman, A.; Lesigne, E.
20
2008
Van der Corput sets in \(\mathbb Z^d\). Zbl 1177.37018
Bergelson, Vitaly; Lesigne, Emmanuel
10
2008
Some new results in multiplicative and additive Ramsey theory. Zbl 1136.05074
Beiglböck, Mathias; Bergelson, Vitaly; Hindman, Neil; Strauss, Dona
7
2008
Ledrappier’s system is almost mixing of all orders. Zbl 1154.37300
Arenas-Carmona, L.; Berend, D.; Bergelson, V.
5
2008
Distribution of values of bounded generalized polynomials. Zbl 1137.37005
Bergelson, Vitaly; Leibman, Alexander
33
2007
Central sets and a non-commutative Roth theorem. Zbl 1201.37003
Bergelson, V.; McCutcheon, R.
15
2007
Complexities of finite families of polynomials, Weyl systems, and constructions in combinatorial number theory. Zbl 1146.37007
Bergelson, V.; Leibman, A.; Lesigne, E.
6
2007
Ergodicity and mixing of non-commuting epimorphisms. Zbl 1127.37007
Bergelson, Vitaly; Gorodnik, Alexander
4
2007
Some historical remarks and modern questions around the ergodic theorem. Zbl 1282.01010
Bergelson, Vitaly
1
2007
Multiplicative structures in additively large sets. Zbl 1105.05071
Beiglböck, Mathias; Bergelson, Vitaly; Hindman, Neil; Strauss, Dona
19
2006
Piecewise-Bohr sets of integers and combinatorial number theory. Zbl 1114.37008
Bergelson, Vitaly; Furstenberg, Hillel; Weiss, Benjamin
17
2006
Combinatorial and Diophantine applications of ergodic theory. (With Appendix A by A. Leibman, with Appendix B by Anthony Quas and Máté Wierdl). Zbl 1130.37317
Bergelson, Vitaly
14
2006
IP-systems, generalized polynomials and recurrence. Zbl 1107.37007
Bergelson, Vitaly; Knutson, Inger J.; McCutcheon, Randall
9
2006
Affine actions of a free semigroup on the real line. Zbl 1143.37006
Bergelson, Vitaly; Misiurewicz, Michał; Senti, Samuel
5
2006
Ergodic Ramsey theory: a dynamical approach to static theorems. Zbl 1122.28011
Bergelson, Vitaly
2
2006
Multiple recurrence and nilsequences (with an appendix by Imre Ruzsa). Zbl 1087.28007
Bergelson, Vitaly; Host, Bernard; Kra, Bryna
66
2005
Multiplicatively large sets and ergodic Ramsey theory. Zbl 1093.11003
Bergelson, Vitaly
10
2005
Polynomial Szemerédi theorems for countable modules over integral domains and finite fields. Zbl 1087.11007
Bergelson, V.; Leibman, A.; McCutcheon, R.
9
2005
Simultaneous Diophantine approximation and VIP systems. Zbl 1142.11048
Bergelson, Vitaly; Håland Knutson, Inger J.; McCutcheon, Randall
3
2005
Failure of the Roth theorem for solvable groups of exponential growth. Zbl 1115.37003
Bergelson, V.; Leibman, A.
6
2004
Weakly mixing group actions: a brief survey and an example. Zbl 1161.37006
Bergelson, V.; Gorodnik, A.
5
2004
Minimal idempotents and ergodic Ramsey theory. Zbl 1039.05063
Bergelson, Vitaly
27
2003
Topological multiple recurrence for polynomial configurations in nilpotent groups. Zbl 1016.05070
Bergelson, V.; Leibman, A.
6
2003
A nilpotent Roth theorem. Zbl 1042.37001
Bergelson, V.; Leibman, A.
14
2002
Squarefree numbers, IP sets and ergodic theory. Zbl 1042.11006
Bergelson, V.; Ruzsa, I.
4
2002
Partition regular structures contained in large sets are abundant. Zbl 0966.05078
Bergelson, Vitaly; Hindman, Neil
19
2001
A Krengel-type theorem for finitely-generated nilpotent groups. Zbl 1007.47006
Bergelson, V.; Kornfeld, I.; Leibman, A.; Mityagin, B.
1
2001
An ergodic IP polynomial Szemerédi theorem. Zbl 0948.28010
Bergelson, Vitaly; McCutcheon, Randall
27
2000
Aspects of uniformity in recurrence. Zbl 0966.28009
Bergelson, Vitaly; Host, Bernard; McCutcheon, Randall; Parreau, François
12
2000
Ergodic theory and diophantine problems. Zbl 0972.37008
Bergelson, Vitaly
10
2000
The multifarious Poincaré recurrence theorem. Zbl 0957.05105
Bergelson, Vitaly
8
2000
Set-polynomials and polynomial extension of the Hales-Jewett theorem. Zbl 0969.05061
Bergelson, V.; Leibman, A.
24
1999
Additive and multiplicative Ramsey theory in the reals and the rationals. Zbl 0917.05080
Bergelson, Vitaly; Hindman, Neil; Leader, Imre
6
1999
Notions of size and combinatorial properties of quotient sets in semigroups. Zbl 0946.22002
Bergelson, Vitaly; Hindman, Neil; McCutcheon, Randall
23
1998
Recurrence for semigroup actions and a non-commutative Schur theorem. Zbl 0905.28010
Bergelson, V.; McCutcheon, R.
13
1998
A Roth theorem for amenable groups. Zbl 0886.43002
Bergelson, Vitaly; McCutcheon, Randall; Zhang, Qing
17
1997
All-sums sets in \((0,1]\)-category and measure. Zbl 0884.28005
Bergelson, Vitaly; Hindman, Neil; Weiss, Benjamin
2
1997
Dense difference sets and their combinatorial structure. Zbl 0868.05009
Bergelson, Vitaly; Erdős, Paul; Hindman, Neil; Łuczak, Tomasz
1
1997
Polynomial extensions of van der Waerden’s and Szemerédi’s theorems. Zbl 0870.11015
Bergelson, V.; Leibman, A.
109
1996
Ergodic Ramsey theory – an update. Zbl 0846.05095
Bergelson, Vitaly
45
1996
IP-sets and polynomial recurrence. Zbl 0958.28013
Bergelson, Vitaly; Furstenberg, Hillel; McCutcheon, Randall
20
1996
Sets of recurrence and generalized polynomials. Zbl 0958.28014
Bergelson, Vitaly; Håland, Inger Johanne
8
1996
Uniformity in the polynomial Szemerédi theorem. Zbl 0862.28014
Bergelson, Vitaly; McCutcheon, Randall
7
1996
Iterated spectra of numbers—elementary, dynamical, and algebraic approaches. Zbl 0855.05098
Bergelson, Vitaly; Hindman, Neil; Kra, Bryna
5
1996
Sets partition regular for \(n\) equations need not solve \(n+1\). Zbl 0859.04001
Bergelson, Vitaly; Hindman, Neil; Leader, Imre
3
1996
Convergence in ergodic theory and probability. Papers from the conference, Ohio State University, Columbus, OH, USA, June 23–26, 1993. Zbl 0846.00030
Bergelson, V. (ed.); March, P. (ed.); Rosenblatt, J. (ed.)
3
1996
Partition theorems for spaces of variable words. Zbl 0809.04005
Bergelson, Vitaly; Blass, Andreas; Hindman, Neil
23
1994
On \(\text{IP}^*\) sets and central sets. Zbl 0820.05061
Bergelson, Vitaly; Hindman, Neil
11
1994
Some results on nonlinear recurrence. Zbl 0803.28011
Bergelson, V.; Boshernitzan, M.; Bourgain, J.
11
1994
Rado’s theorem for commutative rings. Zbl 0795.05140
Bergelson, Vitaly; Deuber, Walter; Hindman, Neil; Lefmann, Hanno
4
1994
Weakly wandering vectors for unitary actions of commutative groups. Zbl 0841.22004
Bergelson, Vitaly; Kornfeld, Isaac; Mityagin, Boris
1
1994
Additive and multiplicative Ramsey theorems in \(\mathbb{N}\)—some elementary results. Zbl 0794.05127
Bergelson, Vitaly; Hindman, Neil
7
1993
Multiplicative subgroups of finite index in a ring. Zbl 0784.12002
Bergelson, Vitaly; Shapiro, Daniel B.
10
1992
Ramsey theory in noncommutative semigroups. Zbl 0757.05009
Bergelson, Vitaly; Hindman, Neil
7
1992
Some topological semicommutative van der Waerden type theorems and their combinatorial consequences. Zbl 0761.05008
Bergelson, Vitaly; Hindman, Neil
7
1992
Rado’s theorem for finite fields. Zbl 0838.05009
Bergelson, V.; Deuber, W. A.; Hindman, N.
5
1992
Nonmetrizable topological dynamics and Ramsey theory. Zbl 0725.22001
Bergelson, Vitaly; Hindman, Neil
45
1990
Ultrafilters and multidimensional Ramsey theorems. Zbl 0693.05007
Bergelson, V.; Hindman, N.
6
1989
An algebraic proof of van der Waerden’s theorem. Zbl 0704.22004
Bergelson, Vitaly; Furstenberg, Hillel; Hindman, Neil; Katznelson, Yitzhak
4
1989
...and 14 more Documents
all top 5

Cited by 458 Authors

66 Bergelson, Vitaly
47 Hindman, Neil
23 Strauss, Dona
22 Frantzikinakis, Nikos
19 Leibman, Alexander
17 Tao, Terence
14 Host, Bernard
14 Kra, Bryna
14 Ziegler, Tamar
13 McCutcheon, Randall
9 Moreira, Joel
9 Sun, Wenbo
9 Ye, Xiangdong
8 Austin, Tim D.
8 Di Nasso, Mauro
8 Eisner, Tanja
8 Green, Ben Joseph
8 Huang, Wen
8 Jin, Renling
8 Koutsogiannis, Andreas
8 Richter, Florian Karl
7 Brian, William Rea
7 Kifer, Yuri
7 Robertson, Donald
7 Wierdl, Máté
7 Zorin-Kranich, Pavel
6 Beiglböck, Mathias
6 Berend, Daniel
6 Donoso, Sebastián
6 Fish, Alexander
6 Leader, Imre
6 Lemańczyk, Mariusz
6 Lesigne, Emmanuel
6 Lupini, Martino
6 Patra, Sourav Kanti
6 Shao, Song
5 Konieczny, Jakub
5 Li, Hanfeng
5 Maass, Alejandro
5 Rapinchuk, Andrei S.
4 Byszewski, Jakub
4 Chu, Qing
4 Dai, Xiongping
4 Glasscock, Daniel
4 Goldbring, Isaac
4 Gowers, William Timothy
4 Grivaux, Sophie
4 Madritsch, Manfred G.
4 Son, Younghwan
4 Tyros, Konstantinos
4 Zamboni, Luca Quardo
3 Assani, Idris
3 Baglini, Lorenzo Luperi
3 Björklund, Michael
3 del Junco, Andres
3 Deuber, Walter A.
3 Downarowicz, Tomasz
3 Farmaki, Vassiliki
3 Fox, Jacob
3 Goswami, Sayan
3 Johnson, John H. jun
3 Jungić, Veselin M.
3 Karageorgos, Dimitris
3 Kazhdan, David A.
3 Kerr, David
3 Kolesnik, Grigoriĭ Abramovich
3 Kułaga-Przymus, Joanna
3 Le, Anh Ngoc
3 Lê, Thái Hoàng
3 Leth, Steven C.
3 Lovett, Shachar
3 Magyar, Akos
3 Mahlburg, Karl
3 McNew, Nathan
3 Müller, Vladimír
3 Nair, Ravindra
3 Petersen, Karl E.
3 Serra, Oriol
3 Szemerédi, Endre
3 Tichy, Robert Franz
3 Vaienti, Sandro
3 Vena, Lluís
3 Wang, Huoyun
3 Wolf, Julia
2 Badea, Catalin
2 Bès, Juan P.
2 Boshernitzan, Michael D.
2 Bucci, Michelangelo
2 Cai, Fangzhou
2 Campbell, James T.
2 Carlson, Timothy J.
2 Chen, Zhijing
2 Conlon, David
2 Dastjerdi, Dawoud Ahmadi
2 De, Dibyendu
2 Debnath, Pintu
2 Derksen, Harm
2 Dodos, Pandelis
2 Dong, Dong
2 Efrat, Ido
...and 358 more Authors
all top 5

Cited in 109 Serials

57 Ergodic Theory and Dynamical Systems
35 Israel Journal of Mathematics
32 Topology and its Applications
31 Journal d’Analyse Mathématique
29 Transactions of the American Mathematical Society
27 Journal of Combinatorial Theory. Series A
22 Advances in Mathematics
20 Proceedings of the American Mathematical Society
17 Semigroup Forum
11 Acta Arithmetica
11 Annals of Mathematics. Second Series
10 Journal of Mathematical Analysis and Applications
10 Journal of Number Theory
9 Combinatorics, Probability and Computing
9 Discrete and Continuous Dynamical Systems
8 Journal of Functional Analysis
8 Indagationes Mathematicae. New Series
7 European Journal of Combinatorics
6 Combinatorica
6 Journal of the American Mathematical Society
6 Geometric and Functional Analysis. GAFA
5 Monatshefte für Mathematik
5 Bulletin of the American Mathematical Society. New Series
5 Comptes Rendus. Mathématique. Académie des Sciences, Paris
4 Acta Mathematica
4 Archiv der Mathematik
4 Fundamenta Mathematicae
4 Inventiones Mathematicae
4 The Journal of Symbolic Logic
3 Discrete Mathematics
3 Annales de l’Institut Fourier
3 Duke Mathematical Journal
3 Illinois Journal of Mathematics
3 Journal of Algebra
3 Journal of Differential Equations
3 Journal für die Reine und Angewandte Mathematik
3 Mathematische Zeitschrift
3 Mathematika
3 Probability Theory and Related Fields
3 Finite Fields and their Applications
3 Journal of the European Mathematical Society (JEMS)
3 Integers
3 Science China. Mathematics
2 American Mathematical Monthly
2 Bulletin of the Australian Mathematical Society
2 Mathematical Notes
2 Mathematical Proceedings of the Cambridge Philosophical Society
2 Rocky Mountain Journal of Mathematics
2 Studia Mathematica
2 Chaos, Solitons and Fractals
2 Glasgow Mathematical Journal
2 Manuscripta Mathematica
2 Mathematische Annalen
2 Memoirs of the American Mathematical Society
2 Graphs and Combinatorics
2 Journal of Theoretical Probability
2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
2 The Electronic Journal of Combinatorics
2 The New York Journal of Mathematics
2 Selecta Mathematica. New Series
2 Forum of Mathematics, Pi
2 Communications in Mathematics and Statistics
1 Communications in Mathematical Physics
1 Journal of Statistical Physics
1 Nonlinearity
1 Russian Mathematical Surveys
1 Mathematics of Computation
1 Journal of Geometry and Physics
1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
1 The Annals of Probability
1 Bulletin of the London Mathematical Society
1 Canadian Journal of Mathematics
1 Commentarii Mathematici Helvetici
1 Czechoslovak Mathematical Journal
1 International Journal of Mathematics and Mathematical Sciences
1 Journal of Combinatorial Theory. Series B
1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
1 Proceedings of the Edinburgh Mathematical Society. Series II
1 Siberian Mathematical Journal
1 Synthese
1 Bulletin of the Korean Mathematical Society
1 Annals of Pure and Applied Logic
1 Physica D
1 Acta Mathematicae Applicatae Sinica. English Series
1 Revista Matemática Iberoamericana
1 Proceedings of the National Academy of Sciences of the United States of America
1 Annales de l’Institut Henri Poincaré. Probabilités et Statistiques
1 Archive for Mathematical Logic
1 Experimental Mathematics
1 Topology Proceedings
1 Journal of Mathematical Sciences (New York)
1 Annales Mathématiques Blaise Pascal
1 Journal of Mathematical Chemistry
1 Abstract and Applied Analysis
1 Journal of Group Theory
1 Annals of Combinatorics
1 Acta Mathematica Sinica. English Series
1 Journal of Dynamical Systems and Geometric Theories
1 ACM Transactions on Computational Logic
1 Cubo
...and 9 more Serials
all top 5

Cited in 39 Fields

252 Dynamical systems and ergodic theory (37-XX)
200 Number theory (11-XX)
179 Combinatorics (05-XX)
89 Measure and integration (28-XX)
78 General topology (54-XX)
72 Topological groups, Lie groups (22-XX)
48 Group theory and generalizations (20-XX)
34 Mathematical logic and foundations (03-XX)
32 Abstract harmonic analysis (43-XX)
21 Probability theory and stochastic processes (60-XX)
19 Operator theory (47-XX)
17 Functional analysis (46-XX)
8 Order, lattices, ordered algebraic structures (06-XX)
8 Field theory and polynomials (12-XX)
8 Harmonic analysis on Euclidean spaces (42-XX)
7 Linear and multilinear algebra; matrix theory (15-XX)
7 Computer science (68-XX)
6 Associative rings and algebras (16-XX)
4 Algebraic geometry (14-XX)
4 \(K\)-theory (19-XX)
3 General algebraic systems (08-XX)
3 Real functions (26-XX)
2 General and overarching topics; collections (00-XX)
2 Difference and functional equations (39-XX)
2 Sequences, series, summability (40-XX)
2 Convex and discrete geometry (52-XX)
2 Differential geometry (53-XX)
2 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
1 History and biography (01-XX)
1 Commutative algebra (13-XX)
1 Nonassociative rings and algebras (17-XX)
1 Functions of a complex variable (30-XX)
1 Ordinary differential equations (34-XX)
1 Integral transforms, operational calculus (44-XX)
1 Algebraic topology (55-XX)
1 Global analysis, analysis on manifolds (58-XX)
1 Quantum theory (81-XX)
1 Statistical mechanics, structure of matter (82-XX)
1 Biology and other natural sciences (92-XX)

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