Convergence of multiple ergodic averages along polynomials of several variables

Israel Journal of Mathematics

Volumn 146, Issue , 2005, Pages 303-315

  Leibman, A ^a  

^a OHIO STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 18444400190     PISSN: 00212172     EISSN: 15658511     Source Type: Journal    
DOI: 10.1007/BF02773538     Document Type: Article

References (15)

1. [B1] V. Bergelson, Weakly mixing PET, Ergodic Theory and Dynamical Systems 7 (1987), 337-349.
2. [B2] V. Bergelson, The multifarious Poincaré recurrence theorem, in Descriptive Set Theory and Dynamical Systems, London Mathematical Society Lecture Note Series 277, Cambridge University Press, Cambridge, 2000, pp. 31-57.
3. [BMQ] V. Bergelson, R. McCutcheon and Q. Zhang, A Roth theorem for amenable groups, American Journal of Mathematics 119 (1997), 1173-1211.
4. [CL1] J.-P. Conze and E. Lesigne, Théorèmes ergodiques pour des mesures diagonales, Bulletin de la Société Mathématique de France 112 (1984), 143-175.
5. [CL2] J.-P. Conze and E. Lesigne, Sur un théorème ergodique pour des mesures diagonales, Publications de l'Institut de Recherche de Mathématiques de Rennes, Probabilités, 1987.
6. [F] H. Furstenberg, Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions, Journal d'Analyse Mathématique 31 (1977), 204-256.
7. n2x), in Convergence in Ergodic Theory and Probability (V. Bergelson, P. March and J. M. Rosenblatt, eds.), Walter de Gruyter, Berlin, 1996, pp. 193-227.
8. [HK1] B. Host and B. Kra, Convergence of Conze-Lesigne averages, Ergodic Theory and Dynamical Systems 21 (2001), 493-509.
9. [HK2] B. Host and B. Kra, Averaging along cubes, in Dynamical Systems and Related Topics, Cambridge University Press, to appear.
10. [HK3] B. Host and B. Kra, Non-conventional ergodic averages and nilmanifolds, Annals of Mathematics, to appear.
11. [HK4] B. Host and B. Kra, Convergence of polynomial ergodic averages, Israel Journal of Mathematics (2005), to appear.
12. d by translations on a nilmanifold, Ergodic Theory and Dynamical Systems, to appear.
13. [L2] A. Leibman, Host-Kra factors for the powers of a transformation, preprint. Available at http://www.math.ohio-state.edu/~leibman/preprints
14. [Z1] T. Ziegler, Nonconventional Ergodic Averages, Ph.D. Thesis, Technion, 2002.
15. [Z2] T. Ziegler, Universal characteristic factors and non-conventional ergodic averages, preprint.