Skip to main content

Advertisement

Log in

On measure rigidity of unipotent subgroups of semisimple groups

  • Published:
Acta Mathematica

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

  • [B]Bowen, R., Weak mixing and unique ergodicity on homogeneous spaces.Israel J. Math., 23 (1976), 267–273.

    MATH  MathSciNet  Google Scholar 

  • [BM]Brezin, J. &Moore, C., Flows on homogeneous spaces: a new look.Amer. J. Math., 103 (1981), 571–613.

    MathSciNet  Google Scholar 

  • [D1]Dani, S. G., Invariant measures of horospherical flows on noncompact homogeneous spaces.Invent. Math., 47 (1978), 101–138.

    Article  MATH  MathSciNet  Google Scholar 

  • [D2]—, Invariant measures and minimal sets of horospherical flows.Invent. Math., 64 (1981), 357–385.

    Article  MATH  MathSciNet  Google Scholar 

  • [EP]Ellis, R. &Perrizo, W., Unique ergodicity of flows on homogeneous spaces.Israel J. Math., 29 (1978), 276–284.

    MathSciNet  Google Scholar 

  • [F1]Furstenberg, H., Strict ergodicity and transformations of the torus.Amer. J. Math., 83 (1961), 573–601.

    MATH  MathSciNet  Google Scholar 

  • [F2]Furstenberg, H., The unique ergodicity of the horocycle flow, inRecent Advances in Topological Dynamics, 95–115. Springer, 1972.

  • [GE]Greenleaf, P. &Emerson, W. R., Group structure and pointwise ergodic theorem for connected amenable groups.Adv. in Math., 14 (1974), 153–172.

    Article  MathSciNet  Google Scholar 

  • [H]Humphreys, J.,Introduction to Lie Algebras and Representation Theory. Springer-Verlag, 1972.

  • [J]Jacobson, N.,Lie Algebras. John Wiley, 1962.

  • [M]Margulis, G. A., Discrete subgroups and ergodic theory.Symposium in honor of A. Selberg, Number theory, trace formulas and discrete groups. Oslo, 1989.

  • [P]Parry, W., Ergodic properties of affine transformations and flows on nilmanifolds.Amer. J. Math., 91 (1969), 757–771.

    MATH  MathSciNet  Google Scholar 

  • [R1]Ratner, M., Rigidity of horocycle flows.Ann. of Math., 115 (1982), 597–614.

    Article  MATH  MathSciNet  Google Scholar 

  • [R2] —, Factors of horocycle flows.Ergodic Theory Dynamical Systems, 2 (1982), 465–489.

    MATH  MathSciNet  Google Scholar 

  • [R3] —, Horocycle flows: joinings and rigidity of products.Ann. of Math., 118 (1983), 277–313.

    Article  MATH  MathSciNet  Google Scholar 

  • [R4] —, Strict measure rigidity for unipotent subgroups of solvable groups.Invent. Math., 101 (1990), 449–482.

    Article  MATH  MathSciNet  Google Scholar 

  • [R5] —, Invariant measures for unipotent translations on homogeneous spaces.Proc. Nat. Acad. Sci. U.S.A., 87 (1990), 4309–4311.

    MATH  MathSciNet  Google Scholar 

  • [Ve]Veech, W., Unique ergodicity of horospherical flows.Amer. J. Math., 99 (1977), 827–859.

    MATH  MathSciNet  Google Scholar 

  • [W1]Witte, D., Rigidity of some translations on homogeneous spaces.Invent. Math., 81 (1985), 1–27.

    Article  MATH  MathSciNet  Google Scholar 

  • [W2] —, Zero entropy affine maps on homogeneous spaces.Amer. J. Math., 109 (1987), 927–961.

    MATH  MathSciNet  Google Scholar 

  • [W3]Witte, D., Measurable quotients of unipotent translations on homogeneous spaces. To appear.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Partially supported by Guggenheim Foundation Fellowship and NSF Grant DMS-8701840.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ratner, M. On measure rigidity of unipotent subgroups of semisimple groups. Acta Math. 165, 229–309 (1990). https://doi.org/10.1007/BF02391906

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02391906

Keywords

Navigation