Bernoulli an Translations and Minimal Horospheres on Homogeneous Spaces

Jump To References Section

Authors

  • S. G. Dani
     Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005 ,IN

Abstract

Let M = G/⌈ be a homogeneous space where G is a Lie group and ⌈ is a lattice in G, i.e. a discrete subgroup of G such that G/⌈ admits a finite G-invariant Borel measure.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Downloads

Published

1976-12-01

How to Cite

Dani, S. G. (1976). Bernoulli an Translations and Minimal Horospheres on Homogeneous Spaces. The Journal of the Indian Mathematical Society, 40(1-4), 245–284. Retrieved from https://informaticsjournals.co.in/index.php/jims/article/view/16630

Issue

Volume 40, Issue 1-4, March-December 1976

Section

Articles

License

Copyright (c) 1976 S. G. Dani

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

References

ANOSOV, D. V. Geodesic flows on closed Riemann manifolds of negative curvature, Trudy Mat. Inst. Steklov 90 (1967), 210, (Russian)=Proceedings of the Steklov Inst, of Math., 90 (1967).

AZENCOTT, R. Diffeomorphisms d'Anosov et schemas de Bernoulli, C. R. Acad. Sci. Paris Ser A-B 270 (1970), A 1105-A 1107.

BOREL, A. Linear algebraic groups. W. A. Benjamin, New York, 1969.

, Compact Clifford Klein forms on symmetric spaces, Topology 2(1963), 111-122.

BOWEN, R. Markov partitions for Axiom A diffeomorphisms, Amer. J. Math. 92(1970), 72-74.

, Entropy for group endomorphisms and homogeneous spaces, Trim. Amer. Math. Soc. 153 (1971), 401-414.

BRUHAT, F. Lectures on some aspects of p-adic analysis, TIFR, Bombay.

DANI, J. S. Density properties of orbits under discrete group,/. Ind. Math. Soc, 39 (1975), 189-218.

DANI J. S. andS. G. DANI. Discrete groups with dense orbits, /. Ind. Math. Soc. 37(1973),183-195.

DANI S. G. Kolmogorov automorphisms on homogeneous spaces, Amer. J. Math., 98(1976), 119-163.

GELFAND, I. M. Automorphic functions and theory of representations, Proc. Internat. Cong, of Mathematicians, 1962, Inst. Mittag-Leffler, Stockholm, 1963.

GREENBERG, L. Discrete groups with dense orbits: Flows on homogeneous spaces, Ann. Math. Studies, No. 53, pp. 85-103.

JACOBSON, N. Lie algebras, Interscience, New York, 1962.

KIRILOV, A. A. Dynamical systems, factors and representations of groups, Uspekhi Mat. Nauk 22, 5 (1967), 67-80, (Russian) = Russ. Math. Surveys 22 (1967), 63-75.

KUSHNIRENKO, A. G. On metric invariants of entropy type, Uspekhi Mat. Nauk 22, 5 (1967), 57-66 (Russian)-*!/.^. Math. Surveys 22 (1967), 53-61.

, An upper bound of the entropy of a classical dynamical system, Dokl. Akad. Nauk SSSR 161 (1965), 37-38, (Russian) = Soviet Math. Dokl. 6 (1965) 360-362.

MOORE, C. C. Ergodicity of flows on homogeneous spaces, Amer. J. Math. 88 (1966), 154-178.

MOSTOW, G. D. Intersection of discrete subgroups with Cartan subgroups, /. Ind. Math. Soc. 34 (1970), 203-214.

ORNSTEIN, D. S. and B. WEISS, Geodesic flows are Bemoullian, Israeli. Math. 14(1973), 184-198.

ORNSTEIN D. S. Bernoulli shifts with the same entropy are isomorphic, Advances in Math. 4 (1969), 337-3 52.

, Imbedding Bernoulli shifts in flows. Contributions to Ergodic Theory and Probability, Lecture Notes in Math., Springer-Verlag, Berlin. (1970), 178-218.

, Two Bernoulli shifts with infinite entropy are isomorphic, Advances in Math. 5 (1970), 339-348.

, Factors of Bernoulli shifts are Bernoulli shifts, Advances in Math. 5 (1970), 349-364.

PLATANOV, V. P. The problem of strong approximation and the Kneser-Tits. conjecture. Izv Akad. Nauk SSSR (Ser. Mat.) 33 (1969). 1211-1219. Complements, ibid. 34(1970), 775-777.

PRASAD, GOPAL and M.S. RAOHUNATHAN, Cartan subgroups and lattices in semisimple groups, Ann. Math. 96 (1972), 296-317.

RAGHUNATHAN, M. S. Discrete subgroups of Lie groups, Band 68, SpringerVerlag, Berlin, 1972.

ROHLIN, V. I. On the fundamental ideas of measure theory, Math. Sb. 25(1949), 107-150 (Russian) = Amer. Math. Soc. Transl. (1), 10(1962), 1-54.

SERRE, J. P. Lie algebras and Lie groups, W. A. Benjamin, New York, 1965.

SINAI, JA. G. Dynamical systems with countable multiple Lebesgue spectrum II, Izv. Akad. Nauk SSSR (Ser. Mat.) 30(1966), 15-68 (Russian) = Amer. Math. Soc. Transl. (2) 68 (1968), 34-88.

SMORODINSKY, M. Ergodic theory; entropy. Lecture Notes in Math. 214, Springer-Verlag, Berlin, 1971.

STEPIN, A. M. Dynamical systems on homogeneous spaces of semisimple Lie groups, Izv. Akad. Nauk, SSSR (Ser. Mat.) 37 (1973), 1091-1107.

TAMAGAWA, T. On discrete subgroups of p-adic algebraic groups, Arithmetical Algebraic Geometry Proceedings, Purdue, Indiana, 1963, 11-17.

THOMAS, R. K. Metric properties of transformations on G-spaces, Trans. Amer. Math. Soc. 168 (1971), 103-117.

TOMTER, PER, Anosov flows on infra-homogeneous spaces. Proceedings of Symposia in Pure Math., Vol. 14, Global Analysis, Amer. Math. Soc, Providence, Rhode Island, (1970), 299-327.

WEIL, A. Discrete subgroups of Lie groups II, Ann. Math. 75 (1962), 578-602.