Pointwise convergence of ergodic averages for polynomial sequences of translations on a nilmanifold

Ergodic Theory and Dynamical Systems

Volumn 25, Issue 1, 2005, Pages 201-213

  Leibman, A ^a  

^a OHIO STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 13444272018     PISSN: 01433857     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0143385704000215     Document Type: Article

References (13)

1. [AGH] L. Auslander, L. Green and F. Hahn. Flows on Homogeneous Spaces (Annals of Mathematical Studies, 53). Princeton University Press, Princeton, NJ, 1963.
2. [BL] V. Bergelson and A. Leibman. A nilpotent Roth theorem. Invent. Math. 147(2) (2002), 429-470.
3. [F] H. Furstenberg. Recurrence in Ergodic Theory and Combinatorial Number Theory. Princeton University Press, Princeton, NJ, 1981.
4. [L1] A. Leibman. Multiple recurrence theorem for nilpotent group actions. Geom. Funct. Anal. 4 (1994), 648-659.
5. [L2] A. Leibman. Multiple recurrence theorem for measure preserving actions of a nilpotent group. Geom. Funct. Anal 8 (1998), 853-931.
6. [Le] E. Lesigne. Sur une nil-variété, les parties minimales associées à une translation sont uniquement ergodiques. Ergod. Th. & Dynam. Sys. 11 (1991), 379-391.
7. [M] A. Malcev. On a class of homogeneous spaces. Izvestiya Akad. Nauk SSSR, Ser. Mat. 13(1949), 9-32.
8. [MZ] D. Montgomery and L. Zippin. Topological Transformation Groups. Interscience, New York, 1955.
9. [P1] W. Parry. Ergodic properties of affine transformations and flows on nilmanifolds. Amer. J. Math. 91 (1969), 757-771.
10. [P2] W. Parry. Dynamical systems on nilmanifolds. Bull. London Math. Soc. 2 (1970), 37-40.
11. [R] M. Ratner. Raghunatan's topological conjecture and distribution of unipotent flows. Duke Math. J. 61(1) (1991), 235-280.
12. [Sh1] N. Shah. Limit distributions of polynomial trajectories on homogeneous spaces. Duke Math. J. 75(3) (1994), 711-732.
13. [Sh2] N. Shah. Invariant measures and orbit closures on homogeneous spaces for actions of subgroups generated by unipotent elements. Lie Groups and Ergodic Theory (Mumbai, 1996). Tata Institute of Fundamental Research, Bombay, 1998, pp. 229-271.