Article PDF
Avoid common mistakes on your manuscript.
References
[B-Z] Bernstein, I.N., Zelevinski, A.V.: Representation of the group GL(n, F) whereF is a non-archimedean local field. Russ. Math. Surv.31.3, 1–68 (1976)
[Bo1] Borel, A.: Linear Algebraic Groups, second enlarged edition. Berlin Heidelberg New York: Springer 1991
[Bo2] Borel, A.: Density properties of certain subgroups of semisimple groups. Ann. Math.72, 179–188 (1960)
[Bo-Pra] Borel, A., Prasad, G.: Values of isotropic quadratic gorms atS-integral points. Compos. Math.83, 347–372 (1992)
[Bo-Spr] Borel, A., Springer, T.A.: Rationality properties of linear algebraic groups. Tôhoku Math. J.20, 443–497 (1968)
[D1] Dani, S.G.: Invariant measures of horospherical flows on noncompact homogeneous spaces. Invent. Math.47, 101–138 (1978)
[D2] Dani, S.G.: On invariant measures, minimal sets, and a lemma of Margulis. Invent. Math.51, 239–260 (1979)
[D3] Dani, S.G.: Invariant measures and minimal sets of horospherical flows. Invent. Math.64, 357–385 (1981)
[D4] Dani, S.G.: On orbits of unipotent flows on homogeneous spaces. Ergod. Th. Dyn. Syst. 4, 25–34 (1984)
[D5] Dani, S.G.: On orbits of unipotent flows on homogeneous spaces — II. Ergod. Th. Dyn. Syst. 6, 167–182 (1986)
[D-Mar1] Dani, S.G., Margulis, G.A.: Values of quadratic forms at primitive integral points. Invent. Math.98, 405–424 (1989)
[D-Mar2] Dani, S.G., Margulis, G.A.: Orbit closures of generic unipotent flows on homogeneous spaces of SL(3,R). Math. Ann.286, 101–128 (1990)
[D-Mar3] Dani, S.G., Margulis, G.A.: Values of quadratic forms at integral points; an elementary approach. Enseign. Math.36, 143–174 (1990)
[D-Mar4] Dani, S.G., Margulis, G.A.: Asymptotic behavior of trajectories of unipotent flows on homogeneous spaces. Proc. Indian Acad. Sci. Math. Sci.101, 1–17 (1991)
[D-Mar5] Dani, S.G., Margulis, G.A.: On the limit distributions of orbits of unipotent flows and integral solutions of quadratic inequalities. C.R. Acad. Sci., Paris, Ser. I314, 698–704 (1992)
[D-Mar6] Dani, S.G., Margulis, G.A.: Limit distributions of orbits of unipotent flows and values of quadratic forms (to appear)
[D-Smi] Dani, S.G., Mmillie, J.: Uniform distribution of horocycle flows for Fuchsian groups. Duke Math. J.51, 185–194 (1984)
[Led-Str] Ledrapier, F., Strelcyn, J.-M.: A proof of the estimation from below in Pesin's entropy formula. Ergodic Theory Dyn. Syst.2, 203–219 (1982)
[Led-Y] Ledrapier, F., Young, L.-S.: The metric entropy of diffeomorphisms. I. Ann. Math.122, 503–539 (1985)
[Ma] Mañé, R.: A proof of Pesin's formula. Ergodic Theory Dyn. Syst.1, 95–102 (1981)
[Mar1] margulis, G.A.: On the action of unipotent groups in the space of lattices. In: Gelfand, I.M. (ed.) Proc. of the summer school on group representations. Bolyai Janos Math. Soc., Budapest, 1971, pp. 365–370. Budapest: Akadémiai Kiado 1975
[Mar2] margulis, G.A.: Formes quadratiques indefinies et flots unipotents sur les espaces homogénes. C.R. Acad. Sci., Paris, Ser. I304, 249–253 (1987)
[Mar3] Margulis, G.A.: Discrete subgroups and ergodic theory. In: Aubert, K.E. et al. (eds.) Proc. of the conference “Number theory, trace formula and discrete groups” in honor of A. Selberg. Oslo 1987, pp. 377–388. London New York: Academic Press 1988
[Mar4] Margulis, G.A.: Orbits of group actions and values of quadrtic forms at integral points. In: Festschrift in honour of I.I. Piatetski-Shapiro. (Isr. Math. Conf. Proc., vol. 3, pp. 127–151) Jerusalem: The Weizmann Science Press of Israel 1990
[Mar5] margulis, G.A.: Discrete Subgroups of Semisimple Groups. Berin Heidelberg New York: Springer 1990
[Mar6] Margulis, G.A.: Dynamical and ergodic properties of subgroup actions on homogeneous spaces with applications in number theory. In: Sutake, I. (ed.) Proceedings of the International Congress of Mathematicians. Kyoto 1990, pp. 193–215, Tokyo: The Mathematical Society of Japan and Berlin Heidelberg New York: Springer 1991
[Mar-To] Margulis, G.A., Tomanov, G.M.: Measure rigidity for algebraic groups over local fields. C.R. Acad. Sci., Paris315, 1221–1226 (1992)
[Mo] Moore, C.C.: The Mautner phenomenon for general unitary representations. Pac. J. Math.86, 155–169 (1980)
[Pral] Prasad, G.: Elementary proof of a theorem of Bruhat-Tits-Rousseau and a theorem of Tits. Bull. Sci. Math. Fr.110, 197–202 (1982)
[Pra2] Prasad, G.: Ratner's Theorem in S-arithmetic setting. In: Workshop on Lie Groups, Ergodic Theory and Geometry. (Publ., Math. Sci. Res. Inst., p. 53) Berlin Heidelberg New York: Springer 1992
[R1] Ratner, M.: Horocycle flows: joining and rigidity of products. Ann. Math.118, 277–313 (1983)
[R2] Ratner, M.: Strict measure rigidity for unipotent subgroups of solvable groups. Invent. Math.101, 449–482 (1990)
[R3] Ratner, M.: On measure rigidity of unipotent subgroups of semi-simple groups. Acta. Math.165, 229–309 (1990)
[R4] Ratner, M.: On Raghunathan's measure conjecture. Ann. Math.134, 545–607 (1992)
[R5] Ratner, M.: Raghunathan topological conjecture and distributions of unipotent flows. Duke Math. J.63, 235–280 (1991)
[R6] Ratner, M.: Invariant measures and orbit closures for unipotent actions on homogeneous spaces. (Publ., Math. Sci. Res. Inst.) Berlin Heidelberg New York: Springer (to appear)
[R7] Ratner, M.: Raghunathan's conjectures forp-adic Lie Groups. Int. Math. Research Notices. Number 5, 141–146 (1993) (in Duke Math. J. 70:2)
[Roh] Rohlin, V.A.: Lectures on the theory of entropy of transformations with invariant measures. Russ. Math. Surv.22:5, 1–54 (1967)
[Sh] Shah, N.: Uniformly distributed orbits of certain flows on homogeneous spaces. Math. Ann.289, 315–334 (1991)
[Tem] Tempelman, A.: Ergodic Theorems for Group Actions. Dordrecht Boston London: Kluwer 1992
[W] Witte, D.: Rigidity of some translations on homogeneous spaces. Invent Math.81, 1–27 (1985)
[Zi] Zimmer, R.: Ergodic Theory and Semisimple Groups. Boston Basel Stuttgart: Birkhäuser 1984
Author information
Authors and Affiliations
Additional information
Dedicated to Armand Borel
On leave from the Institute of Information Transmission of Russian Academy of Science
Oblatum 6-IV-1993
Rights and permissions
About this article
Cite this article
Margulis, G.A., Tomanov, G.M. Invariant measures for actions of unipotent groups over local fields on homogeneous spaces. Invent Math 116, 347–392 (1994). https://doi.org/10.1007/BF01231565
Issue Date:
DOI: https://doi.org/10.1007/BF01231565