Multiple recurrence and nilsequences

Inventiones Mathematicae

Volumn 160, Issue 2, 2005, Pages 261-303

  Bergelson, Vitaly ^a   Host, Bernard ^b   Kra, Bryna ^c   Ruzsa, Imre ^d  

^a OHIO STATE UNIVERSITY   (United States)

^b UNIVERSITÉ GUSTAVE EIFFEL   (France)

^c NORTHWESTERN UNIVERSITY   (United States)

^d INSTITUTE OF EXPERIMENTAL MEDICINE   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17444412724     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00222-004-0428-6     Document Type: Article

References (19)

1. [AGH] Auslander, L., Green, L., Hahn, F.: Flows on homogeneous spaces. Ann. Math. Stud. 53 Princeton: Princeton Univ. Press 1963
2. [Beh] Behrend, F. A.: On sets of integers which contain no three in arithmetic progression. Proc. Natl. Acad. Sci. 23, 331-332 (1946)
3. [Ber] Bergelson, V.: Weakly mixing PET. Ergodic Theory Dyn. Syst. 7, 337-349 (1987)
4. [F3] Furstenberg, H.: Strict ergodicity and transformation of the torus. Am. J. Math. 83, 573-601 (1961)
5. [F1] Furstenberg, H.: Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions. J. Anal. Math. 31, 204-256 (1977)
6. [F2] Furstenberg, H.: Recurrence in Ergodic Theory and Combinatorial Number Theory. Princeton: Princeton Univ. Press (1981)
7. [HK] Host, B., Kra, B.: Nonconventional ergodic averages and nilmanifolds. To appear in Ann. Math. Available at http://www.math.psu.edu/kra (2002)
8. [K] Khintchine, A.Y.: Eine Verschärfung des Poincaréschen "Wiederkehr-Satzes". Compos. Math. 1, 177-179 (1934)
9. [Lei1] Leibman, A.: Polynomial sequences in groups. J. Algebra 201, 189-206 (1998)
10. [Lei2] Leibman, A.: Pointwise convergence of ergodic averages for polynomial sequences of rotations of a nilmanifold. To appear in Ergodic Theory Dyn. Syst. Available at http://www.math.ohio-state.edu/ leibman/preprints (2002)
11. [Les] Lesigne, E.: Sur une nil-variété, les parties minimales associées à une translation sont uniquement ergodiques. Ergodic Theory Dyn. Syst. 11, 379-391 (1991)
12. [M] Malcev, A.: On a class of homogeneous spaces. Am. Math. Soc. Transl. 39 (1951)
13. [Pa1] Parry, W.: Ergodic properties of affine transformations and flows on nilmanifolds. Am. J. Math. 91, 757-771 (1969)
14. [Pa2] Parry, W.: Dynamical systems on nilmanifolds. Bull. Lond. Math. Soc. 2, 37-40 (1970)
15. [Pe] Petresco, J.: Sur les commutateurs. Math. Z. 61, 348-356 (1954)
16. [R] Rudolph, D. J.: Eigenfunctions of T×S and the Conze-Lesigne algebra. Ergodic Theory and its Connections with Harmonic Analysis, ed. by K. Petersen and I. Salama. New York: Cambridge University Press. 369-432 (1995)
17. [S] Szemerédi, E.: On sets of integers containing no k elements in arithmetic progression. Acta Arith. 27, 199-245 (1975)
18. [Z1] Ziegler, T.: A non-conventional ergodic theorem for a nilsystem. To appear in Ergodic Theory Dyn. Syst. Available at http://www.arxiv.org, math.DS/0204058 v1 (2002)
19. [Z2] Ziegler, T.: Universal characteristic factors and Furstenberg averages. Preprint. Available at http://www.arxiv.org/abs/math.DS/0403212 (2004)