Dynamique des flots unipotents sur les espaces homogènes
Séminaire Bourbaki : volume 1991/92, exposés 745-759, Astérisque, no. 206 (1992), Talk no. 747, p. 93-136
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     author = {Ghys, \'Etienne},
     title = {Dynamique des flots unipotents sur les espaces homog\`enes},
     booktitle = {S\'eminaire Bourbaki : volume 1991/92, expos\'es 745-759},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {206},
     year = {1992},
     note = {talk:747},
     pages = {93-136},
     zbl = {0796.58041},
     mrnumber = {1206065},
     language = {fr},
     url = {http://www.numdam.org/item/SB_1991-1992__34__93_0}
}
Ghys, Étienne. Dynamique des flots unipotents sur les espaces homogènes, in Séminaire Bourbaki : volume 1991/92, exposés 745-759, Astérisque, no. 206 (1992), Talk no. 747, pp. 93-136. http://www.numdam.org/item/SB_1991-1992__34__93_0/

[1] D. V. Anosov - Geodesic flows on compact Riemannian manifolds of negative curvature, Trudy Mat. Inst. Steklova, 90 (1967). | MR 224110 | Zbl 0176.19101

[2] L. Auslander, L. Green and F. Hahn - Flows on homogeneous spaces, Ann. of Math. Studies, Princeton 53 (1963). | Zbl 0106.36802

[3] R. C. Baker, H. P. Schlickewey - Indefinite quadratic forms, Proc. London Math. Soc. 54 (1987). | MR 879392 | Zbl 0588.10019

[4] A. Borel - Introduction aux groupes arithmétiques, Hermann, Paris (1969). | MR 244260 | Zbl 0186.33202

[5] A. Borel et G. Prasad - Valeurs de formes quadratiques aux points entiers, C.R. Acad. Sci. Paris, Série I 307 (1988), 217-220. | MR 956809 | Zbl 0654.10022

[6] R. Bowen - Periodic orbits for hyperbolic flows, Amer. J. Math (1972), 1-30. | MR 298700 | Zbl 0254.58005

[7] R. Bowen - Weak mixing and unique ergodicity on homogeneous spaces, Israel J. Math 23 (1976), 267-273. | MR 407233 | Zbl 0338.43014

[8] R. Bowen and B. Marcus - Unique ergodicity of horospherical foliations, Israel J. Math 26 (1977), 43-67. | MR 451307 | Zbl 0346.58009

[9] J. Brezin and C. Moore - Flows on homogeneous spaces : a newlook, Amer. J. Math. 103 (1981), 571-613. | MR 618325 | Zbl 0506.22008

[10] J. W. S. Cassels - An introduction to diophantine approximations, Cambridge University Press (1957). | MR 87708 | Zbl 0077.04801

[11] J. W. S. Cassels - Rational quadratic forms, Academic Press, London- New York (1978). | MR 522835 | Zbl 0395.10029

[12] J. W. S. Cassels and H. P. F. Swinnerton-Dyer - On the product of three homogeneous linear forms and indefinite ternary quadratic forms, Philos. Trans. Roy. Soc. London, Ser. A, 248 (1955), 73-96. | MR 70653 | Zbl 0065.27905

[13] S. G. Dani - Invariant measures of horospherical flows on non compact homogeneous spaces, Invent. Math. 47 (1978), 101-138. | MR 578655 | Zbl 0368.28021

[14] S. G. Dani - On invariant measures, minimal sets and a lemma of Margulis, Invent. Math. 51 (1979), 239-260. | MR 530631 | Zbl 0415.28008

[15] S. G. Dani - Dynamics of the horocycle flow, bullet. A.M.S. 3 (1980), 1037-1039. | Zbl 0461.58008

[16] S. G. Dani - Invariant measures and minimal sets of horospherical flows, Invent. Math. 64 (1981), 357-385. | MR 629475 | Zbl 0498.58013

[17] S. G. Dani - On uniformly distributed orbits of certain horocyclic flows, Ergodic theory and dynamical systems 2 (1982), 139-158. | MR 693971 | Zbl 0504.22006

[18] S. G. Dani - On orbits of unipotent flows on homogeneous spaces, Ergodic theory and dynamical systems 4 (1984), 25-34. | MR 758891 | Zbl 0557.22008

[19] S. G. Dani - Dynamics of flows on homogeneous spaces : a survey, Proceed. of Colloquio de sistemas dinamicos (Guanajuato, 1983), Aportaciones Mat. 1 (1985), 1-30. | MR 823700 | Zbl 0609.58037

[20] S. G. Dani - Divergent trajectories of flows on homogeneous spaces and diophantine approximation, J. Reine Angew. Math. 359 (1985), 55-89. | MR 794799 | Zbl 0578.22012

[21] S. G. Dani - Orbits of horospherical flows, Duke Math. Journal 53 (1986), 177-188. | MR 835804 | Zbl 0609.58038

[22] S. G. Dani - On orbits of unipotent flows on homogeneous spaces II, Ergodic theory and dynamical systems 6 (1986), 167-182. | MR 857195 | Zbl 0601.22003

[23] S. G. Dani - Dense orbits of horospherical flows, dynamical systems and ergodic theory, Banach center publications, volume 23, Polish Scientific Publishers, Warsaw (1989). | MR 1102713 | Zbl 0701.58050

[24] S. G. Dani and G. A. Margulis - Values of quadratic forms at primitive integral points, C.R. Acad. Sci. Paris, Série I, 308 (1989), 199-203. | MR 986379 | Zbl 0675.10011

[25] S. G. Dani and G. A. Margulis - Values of quadratic forms at primitive integral points, Invent. Math. 98 (1989), 405-424. | MR 1016271 | Zbl 0682.22008

[26] S. G. Dani and G. A. Margulis - Orbit closures of generic unipotent flows on homogeneous spaces of SL(3, R), Math. Ann. 286 (1990), 101-128. | MR 1032925 | Zbl 0679.22007

[27] S. G. Dani and G. A. Margulis - Values of quadratic forms at integral points : an elementary approach, L'enseignement mathématique 36 (1990), 143-174. | MR 1071418 | Zbl 0833.11026

[28] S. G. Dani and J. Smillie - Uniform distribution of horocyclic orbits for Fuchsian groups, Duke Math. Journal 51 (1984), 185-194. | MR 744294 | Zbl 0547.20042

[29] H. Davenport and H. Heilbronn - On indefinite quadratic in five variables, J. London Math. Soc. 21 (1946),, 185-193. | MR 20578 | Zbl 0060.11914

[30] E. B. Dynkin - Semi-simple subalgebras of semi-simple Lie algebras, A.M.S. Transl. (Series 2) 6 (1957), 111-244 | Zbl 0077.03404

[31] E. B. Dynkin - Maximal subgroups of the classical groups, A.M.S. Transl. (Series 2) 6 (1957), 245-378. | Zbl 0077.03403

[32] R. Ellis and W. Perrizo - Unique ergodicity of flows on homogeneous spaces, Israel J. Math. 29 (1978), 276-284. | MR 473095 | Zbl 0383.22004

[33] J. Feldman and D. Ornstein - Semirigidity of horocycle flows over compact surfaces of variable negative curvature, Ergodic theory and dynamical systems 7 (1987), 49-72. | MR 886370 | Zbl 0633.58024

[34] L. Flamino - An extension of Ratner's rigidity theorem to n-dimensional hyperbolic space, Ergodic theory and dynamical systems 7 (1987), 73-92. | MR 886371 | Zbl 0623.57030

[35] H. Furstenberg - Strict ergodicity and transformations of the torus, Amer. J. Math. 83 (1961), 573-601. | MR 133429 | Zbl 0178.38404

[36] H. Furstenberg - The structure of distal flows, Amer. J. Math. 85 (1963), 477-515. | MR 157368 | Zbl 0199.27202

[37] H. Furstenberg - The unique ergodicity of the horocyclic flow, in Recent Advances in Topical Dynamics, 95-115, Springer (1972). | MR 393339 | Zbl 0256.58009

[38] G. Hedlund - Fuchsian groups and transitive horocycles, Duke Math. Journal 2 (1936), 530-542. | JFM 62.0392.03 | MR 1545946

[39] G. Hedlund - Dynamics of geodesic flows, bullet. of the A.M.S. 45 (1939), 241-260. | JFM 65.0793.02

[40] G. Hedlund - Fuchsian groups and mixtures, Ann. of Math. 40 (1939), 370-383. | MR 1503464 | Zbl 0020.40302

[41] E. Hopf - Fuchsian groups and ergodic theory, Trans. A.M.S. 39 (1936), 299-314. | JFM 62.0995.01 | MR 1501848

[42] E. Hopf - Statistik der Geodätische Linien Manigfaltigkeiten Negativer Krümmung, Ber. Voch. Sachs. Akad. Wiss. Leipzig 91 (1939), 261-304. | JFM 65.1413.02 | MR 1464

[43] H. Iwaniec - On indefinite quadratic forms in four variables, Acta Arith. 33 (1977), 209-229. | MR 460235 | Zbl 0315.10016

[44] E. Lesigne - Théorèmes ergodiques pour une translation sur une nilvariété, Ergodic theory and dynamical systems 9 (1989), 115-126. | MR 991492 | Zbl 0651.28014

[45] E. Lesigne - Sur une nil-variété, les parties minimales associées à une translation sont uniquement ergodiques, Ergodic theory and dynamical systems 11 (1991), 379-391. | MR 1116647 | Zbl 0709.28012

[46] B. Marcus - Unique ergodicity of the horocyclic flow : variable curvature case, Israel J. of Math. 21 (1975), 133-144. | MR 407902 | Zbl 0314.58013

[47] B. Marcus - Topological conjugacy of horocycle flows, Amer. J. Math. 105 (1983), 623-632. | MR 704217 | Zbl 0533.58029

[48] G. A. Margulis - On the action of unipotent groups in the space of lattices, Proc. of the summer school on group representations, Bolyai Janos Math. Soc., Budapest (1971), 365-370. | MR 470140 | Zbl 0305.22014

[49] G. A. Margulis - Lie groups and ergodic theory, in Avramov, L.L. (eds) Algebra, some current trends, Proceed. Varna 1986, Springer Lecture Notes in Math. 1352, 130-146. | MR 981823 | Zbl 0667.22005

[50] G. A. Margulis - Formes quadratiques indéfinies et flots unipotents sur les espaces homogènes, C.R. Acad. Sci., Série I, 304 (1987), 249- 253. | MR 882782 | Zbl 0624.10011

[51] G. A. Margulis - Indefinite quadratic forms and unipotent flows on homogeneous spaces, Banach center publications, volume 23, Polish Scientific Publishers, Warsaw (1989). | MR 1102736 | Zbl 0689.10026

[52] G. A. Margulis - Discrete subgroups and ergodic theory, Symposium in honour of A. Selberg, Number theory, trace formulas and discrete groups, Academic Press (1989), 377-398. | MR 993328 | Zbl 0675.10010

[53] G. A. Margulis - Compactnes of minimal closed invariant sets of actions of unipotent groups, Geometria Dedicata 37 (1991), 1-9. | MR 1094225 | Zbl 0733.22005

[54] G. A. Margulis - Orbits of group actions and values of quadratic forms at integral points, Preprint IHES. | MR 1159112

[55] C. Moore - The Mautner phenomenon for general unitary representations, Pacific J. Math. 86 (1980), 155-169. | MR 586875 | Zbl 0446.22014

[56] M. Morse - Recurrent geodesics on a surface of negative curvature, Trans. Amer. Math. Soc. 22 (1921), 84-100 | JFM 48.0786.06 | MR 1501161

[57] A. Oppenheim - The minima of indefinite quaternary quadratic forms of signature 0, Proc. Nat. Acad. Sci. USA 15 (1929), 724- 727. | JFM 55.0722.01

[58] A. Oppenheim - The minima of indefinite quaternary quadratic forms, Ann. of Math. 32 (1931), 271-298. | JFM 57.0193.05 | MR 1502997

[59] A. Oppenheim - Values of quadratic forms, I, II, Quart. J. Math., Oxford Ser. (2) 4 (1953), 54-59, 60-66. | MR 54650 | Zbl 0050.27302

[60] A. Oppenheim - Values of quadratic forms, III, Monatsh. Math. Phys. 57 (1953), 97-101. | MR 56648 | Zbl 0052.04402

[61] J.-P. Otal - Le spectre marqué des longueurs des surfaces à courbure négative, Ann. of Math. 131 (1990), 151-162. | MR 1038361 | Zbl 0699.58018

[62] P. Pansu - Le flot géodésique des variétés riemanniennes à courbure négative, Séminaire Bourbaki, exposé n° 738, février 1991. | Numdam | MR 1157845 | Zbl 0753.58024

[63] W. Parry - Ergodic properties of affine transformations and flows on nilmanifolds, Amer. J. Math. 91 (1969), 757-771. | MR 260975 | Zbl 0183.51503

[64] W. Parry - Metric classification of ergodic nilflows, Amer. J. Math. 93 (1971), 819-828. | MR 284567 | Zbl 0222.22010

[65] J. Plante - Anosov flows, Amer. J. Math. (1972), 729-754. | MR 377930 | Zbl 0257.58007

[66] M. Ratner - Factors of horocyclic flows, Ergodic theory and dynamical systems 2 (1982), 465-489. | MR 721735 | Zbl 0536.58029

[67] M. Ratner - Rigidity of horocycle flows, Ann. of Math. 115 (1982), 597-614. | MR 657240 | Zbl 0506.58030

[68] M. Ratner - Horocyclic flows : joinings and rigidity of products, Ann. of Math. 118 (1983), 277-313. | MR 717825 | Zbl 0556.28020

[69] M. Ratner - Ergodic theory in hyperbolic space, Contemp. Math. 26 (1984), 309-334. | MR 737411 | Zbl 0548.58034

[70] M. Ratner - Invariant measures for unipotent translations on homogeneous spaces, Proc. Nat. Acad. Sci. USA 87 (1990), 4309-4311. | MR 1054166 | Zbl 0819.22004

[71] M. Ratner - Strict measure rigidity for unipotent subgroups of solvable groups, Invent. Math. 101 (1990), 449-482. | MR 1062971 | Zbl 0745.28009

[72] M. Ratner - On measure rigidity of unipotent subgroups of semisimple groups, Acta Mathematica 165 (1990), 229-309. | MR 1075042 | Zbl 0745.28010

[73] M. Ratner - On Raghunathan's measure conjecture, à paraître dans Ann. of Maths. | Zbl 0763.28012

[74] M. Ratner - Raghunathan's topological conjecture and distributions of unipotent flows, Duke Math. J, 63 (1991), 235-280. | MR 1106945 | Zbl 0733.22007

[75] M. Ratner - Distribution rigidity for unipotent actions on homogeneous spaces, bulletetin A.M.S. 24 (1991), 321-325. | MR 1069988 | Zbl 0733.22006

[76] M. Rees - Tangentially distal flows, Israel J. of Math. 15 (1980), 9-31. | MR 576459 | Zbl 0438.58024

[77] P. Sarnak - Asymptotic behaviour of periodic orbits of the horocycle flow and Eisenstein series, Comm. on Pure and Applied Math. 34 (1981), 719-739. | MR 634284 | Zbl 0501.58027

[78] W. M. Schmidt - Diophantine approximations, Lecture Notes in Math. 785, Springer-Verlag.

[79] C. Series - The geometry of Markov numbers, Math. Intelligencer 7 (1985), 20-29. | MR 795536 | Zbl 0566.10024

[80] N. A. Shah - Closures of totally geodesic immersions in manifolds of constant negative curvature in : Proceed. Group theory from a geometrical viewpoint, Trieste 1990, ed. É. Ghys, A. Haefliger, A. Verjovsky, World Scientific (1991). | MR 1170382 | Zbl 0846.53041

[81] K. Sigmund - On the space of invariant measures for hyperbolic flows, Amer. J. Math. 94 (1972), 31-37. | MR 302866 | Zbl 0242.28014

[82] J.-C. Sikorav Valeurs des formes quadratiques indéfinies irrationnelles (d'après G.A. Margulis), Séminaire de théorie des nombres, Paris, 86-87, Ed. C Goldstein, Progress in Math. 81, 307-315, Birkhauser. | MR 1042776 | Zbl 0704.11009

[83] A. N. Starkov - Structure of orbits of homogeneous flows and the Raghunathan conjecture, Russian Math. Surveys 45 (1990), 227-228. | MR 1069361 | Zbl 0722.58034

[84] W. Veech - Unique ergodicity of horospherical flows, Amer. J. Math. 99 (1977), 827-859. | MR 447476 | Zbl 0365.28012

[85] A. Verjovsky - Arithmetic, geometry and dynamics in the unit tangent bundle of the modular orbifold, preprint I.C.T.P.

[86] L. Ya. Vulakh - On minima of rational indefinite quadratic forms, J. Number Theory 21 (1985), 275-285. | MR 814006 | Zbl 0578.10024

[87] G. L. Watson - On indefinite quadratic forms in five variables, Proc. London Math. Soc. (3) 3 (1953), 170-181. | MR 57916 | Zbl 0050.04704

[88] G. L. Watson - On indefinite quadratic forms in three or four variables, J. London Math. Soc. 28 (1953), 239-242. | MR 54652 | Zbl 0050.04702

[89] D. Witte - Rigidity of some translations on homogeneous spaces, Invent. Math. 81 (1985), 1-27. | MR 796188 | Zbl 0571.22007

[90] D. Witte - Zero entropy affine maps on homogeneous spaces, Amer. J. Math. 109 (1987), 927-961. | MR 910358 | Zbl 0653.22005

[91] D. Witte - Rigidity of horospherical foliations, Ergodic theory and dynamical systems 9 (1989), 191-205. | MR 991498 | Zbl 0667.58053

[92] D. Witte - Measurable quotients of unipotent translations on homogeneous spaces, à paraître. | Zbl 0831.28010

[93] A. Zeghib - Laminations et hypersurfaces géodésiques des variétés hyperboliques, Ann. Scient. Éc. Norm. Sup. 24 (1991), 171-188. | Numdam | MR 1097690 | Zbl 0738.53019

[94] A. Zeghib - Systèmes dynamiques autonomes. Partie I : Ensembles invariants des flots d'Anosov algébriques, Prépublication E.N.S. Lyon n° 47 (1991).