Skip to main content
Log in

Orbit closures of generic unipotent flows on homogeneous spaces ofSL(3, ℝ)

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Borel, A.: Introduction aux groupes arithmetiques. Publ. de l'Inst. Math. de l'Univ. de Strassbourg XV. Paris: Hermann 1969

    MATH  Google Scholar 

  2. Borel, A., Tits, J.: Groupes réductifs. Publ. Math. I.H.E.S.27, 55–150 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  3. Dani, S.G.: A simple proof of Borel's density theorem. Math. Z.174, 81–94 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  4. Dani, S.G.: On orbits of unipotent flows on homogeneous spaces. Ergod. Theory Dyn. Syst.4, 25–34 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  5. Dani, S.G.: Divergent trajectories of flows on homogeneous spaces and Diophantine approximation. J. Reine Angew. Math.359, 55–89 (1985)

    MathSciNet  MATH  Google Scholar 

  6. Dani, S.G.: Dynamics of flows on homogeneous spaces. A survey. Proceedings of Coloquio de Systemas Dinamicos (Guanajuato, 1983), Aportacione Mat. 1, Soc. Mat. Mexicana, Mexico City, pp. 1–30, 1985

    MATH  Google Scholar 

  7. Dani, S.G.: On orbits of unipotent flows on homogeneous spaces. II Ergod. Theory Dyn. Syst.6, 167–182 (1986)

    MathSciNet  MATH  Google Scholar 

  8. Dani, S.G.: Orbits of horospherical flows. Duke Math. J.53, 177–188 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  9. Dani, S.G., Margulis, G.A.: Values of quadratic forms at primitive integral points. C.R. Acad. Sci. Paris, Ser. I,308, 199–203 (1989)

    MathSciNet  MATH  Google Scholar 

  10. Dani, S.G., Margulis, G.A.: Values of quadratic forms at primite integral points. Invent. Math.98, 405–424 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  11. Dani, S.G., Margulis, G.A.: Asymptotic behaviour of trajectories of unipotent flows on homogeneous spaces (under preparation)

  12. Dani, S.G., Raghavan, S.: Orbits of Euclidean frames under discrete linear groups. Isr. J. Math.36, 300–320 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  13. Green, L.: Nilflows, measure theory, in: Flows on homogeneous spaces. Ann. Math. Studies. Auslander, L., Green, L., Hahn, F. (eds.). Princeton: Princeton Univ. Press 1963

    Google Scholar 

  14. Hedlund, G.A.: Fuchsion groups and transitive horocycles. Duke Math. J.2, 530–542 (1936)

    Article  MathSciNet  MATH  Google Scholar 

  15. Howe, R., Moore, C.C.: Asymptotic behaviour of unitary representations. J. Funct. Anal.32, 72–96 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  16. Margulis, G.A.: Arithmetic properties of discrete subgroups. Usp. Mat. Nauk29, 49–98 (1974); Russ. Math. Surv.29, 107–156 (1974)

    MathSciNet  MATH  Google Scholar 

  17. Margulis, G.A.: Formes quadratique indefinies et flots unipotents sur les éspaces homogènes. C.R. Acad. Sci. Paris, Ser. I.304, 249–253 (1987)

    MathSciNet  MATH  Google Scholar 

  18. Margulis, G.A.: Lie groups and ergodic theory. In: Algebra — some current trenes. Proceedings (Varna, 1986), pp. 130–146. Berlin Heidelberg New York: Springer 1988

    Chapter  Google Scholar 

  19. Margulis, G.A.: Indefinite quadratic forms and unipotent flows on homogeneous spaces. Proceedings of Semester on Dynamical Systems and Ergodic Theory (Warsaw 1986), Banach Centre Publications, Warsaw (to appear)

  20. Margulis, G.A.: Discrete subgroups and ergodic theory, Proceedings of a Conference in honour of Professor A. Selberg (Oslo, 1987) pp. 377–398, New York London: Academic Press 1989

    MATH  Google Scholar 

  21. Parry, W.: Ergodic properties of affine transformations and flows on nilmanifolds. Am. J. Math.91, 751–771 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  22. Raghunathan, M.S.: Discrete subgroups of Lie groups. Berlin Heidelberg New York: Springer 1972

    Book  MATH  Google Scholar 

  23. Ratner, M.: Invariant measures for unipotent translations on homogeneous spaces (preprint)

  24. Zimmer, R.J.: Orbit spaces of unitary representations, ergodic theory and simple Lie groups. Ann. Math.106, 573–588 (1977)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Dedicated to Hans Grauert

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dani, S.G., Margulis, G.A. Orbit closures of generic unipotent flows on homogeneous spaces ofSL(3, ℝ). Math. Ann. 286, 101–128 (1990). https://doi.org/10.1007/BF01453567

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01453567

Keywords

Navigation