Systèmes dynamiques, groupes de matrices et applications arithmétiques. Préface des éditeurs et introduction par les auteurs. Bibliographie générale et index du volume

Berline, Nicole; Plagne, Alain; Sabbah, Claude

Journées mathématiques X-UPS, Systèmes dynamiques, groupes de matrices et applications arithmétiques (2007), pp. v-xviii.

[Apo90] Apostol, Tom M. Modular functions and Dirichlet series in number theory, Graduate Texts in Math., 41, Springer-Verlag, New York, 1990 | DOI

[BD58] Birch, B. J.; Davenport, H. Quadratic equations in several variables, Proc. Cambridge Philos. Soc., Volume 54 (1958), pp. 135-138 | DOI | MR | Zbl

[BGS85] Ballmann, Werner; Gromov, Mikhael; Schroeder, Viktor Manifolds of nonpositive curvature, Progress in Math., 61, Birkhäuser Boston Inc., Boston, MA, 1985 | DOI

[BM00] Bekka, M. Bachir; Mayer, Matthias Ergodic theory and topological dynamics of group actions on homogeneous spaces, London Math. Soc. Lect. Note Series, 269, Cambridge University Press, Cambridge, 2000 | DOI

[Bor69] Borel, Armand Introduction aux groupes arithmétiques, Actualités Scientifiques et Industrielles, 1341, Hermann, Paris, 1969

[Bre00] Breuillard, E. La conjecture d’Oppenheim et sa version quantitative, Mémoire de DEA, Université Paris VI (2000) (http://www.math.polytechnique.fr/~breuilla/Opp4.ps)

[Béd91] Bédard, Robert Groupes linéaires algébriques, Université de Montréal Centre de Recherches Mathématiques, Montreal, QC, 1991, 149 pages

[Cha50] Chabauty, Claude Limite d’ensembles et géométrie des nombres, Bull. Soc. math. France, Volume 78 (1950), pp. 143-151 | DOI | Numdam | Zbl

[Cou] Courtois, Gilles Sur les valeurs aux entiers des formes quadratiques réelles, Systèmes dynamiques, groupes de matrices et applications arithmétiques (Journées X-UPS), Les Éditions de l’École polytechnique, Palaiseau, 2007 (ce volume) | DOI | Zbl

[CS99] Conway, J. H.; Sloane, N. J. A. Sphere packings, lattices and groups, Grundlehren Math. Wissen., 290, Springer-Verlag, New York, 1999 | DOI

[CSD55] Cassels, J. W. S.; Swinnerton-Dyer, H. P. F. On the product of three homogeneous linear forms and the indefinite ternary quadratic forms, Philos. Trans. Roy. Soc. London Ser. A, Volume 248 (1955), pp. 73-96 | DOI | MR | Zbl

[Dal] Dal’Bo, Françoise Points de vue sur les valeurs aux entiers des formes quadratiques binaires, Systèmes dynamiques, groupes de matrices et applications arithmétiques (Journées X-UPS), Les Éditions de l’École polytechnique, Palaiseau, 2007 (ce volume) | DOI

[Dal07a] Dal’Bo, Françoise Trajectoires géodésiques et horocycliques, Savoirs Actuels, CNRS Éditions & EDP Sciences, Paris, 2007 | MR

[Dal07b] Dal’Bo, Françoise Des trajectoires pour approcher les nombres, Pour la Science, Volume 359 (2007)

[Dan01] Dani, S. G. On the Oppenheim conjecture on values of quadratic forms, Essays on geometry and related topics (Monogr. Enseign. Math.), Volume 38, Enseignement Math., Genève, 2001, pp. 257-270 | MR | Zbl

[DH46] Davenport, H.; Heilbronn, H. On indefinite quadratic forms in five variables, J. London Math. Soc., Volume 21 (1946), pp. 185-193 | DOI | MR | Zbl

[Die74] Dieudonné, J. Éléments d’analyse. Tome II : Chapitres XII à XV, Cahiers Scientifiques, XXXI, Gauthier-Villars, Paris, 1974

[DM90] Dani, S. G.; Margulis, G. A. Values of quadratic forms at integral points : an elementary approach, Enseign. Math. (2), Volume 36 (1990) no. 1-2, pp. 143-174 | MR | Zbl

[DN02] Dani, S. G.; Nogueira, Arnaldo On orbits of $\mathrm{SL}{(2,\mathbb{Z})}_{+}$ and values of binary quadratic forms on positive integral pairs, J. Number Theory, Volume 95 (2002) no. 2, pp. 313-328 | MR | Zbl

[DR59] Davenport, H.; Ridout, D. Indefinite quadratic forms, Proc. London Math. Soc. (3), Volume 9 (1959), pp. 544-555 | DOI | MR | Zbl

[Ebe96] Eberlein, Patrick B. Geometry of nonpositively curved manifolds, Chicago Lectures in Math., University of Chicago Press, Chicago, IL, 1996 | MR

[EKL06] Einsiedler, Manfred; Katok, Anatole; Lindenstrauss, Elon Invariant measures and the set of exceptions to Littlewood’s conjecture, Ann. of Math. (2), Volume 164 (2006) no. 2, pp. 513-560 | DOI | MR | Zbl

[EMM98] Eskin, Alex; Margulis, Gregory; Mozes, Shahar Upper bounds and asymptotics in a quantitative version of the Oppenheim conjecture, Ann. of Math. (2), Volume 147 (1998) no. 1, pp. 93-141 | DOI | MR | Zbl

[Fer] Ferréol, Robert Encyclopédie des formes mathématiques remarquables (http://www.mathcurve.com/courbes3d/noeuds/noeuddetrefle.shtml)

[GdlH90] Ghys, Étienne; de la Harpe, Pierre Sur les groupes hyperboliques d’après Mikhael Gromov, Progress in Math., 83, Birkhäuser Boston, Boston, MA, 1990, pp. 1-25 | DOI

[Ghy92] Ghys, Étienne Dynamique des flots unipotents sur les espaces homogènes, Séminaire Bourbaki, Vol. 1991/92 (Astérisque), Volume 206, Société Mathématique de France, Paris, 1992, pp. 93-136 (Exp. no. 747) | Numdam | MR | Zbl

[GL06] Ghys, Étienne; Leys, J. Lorenz and modular flows : a visual introduction, 2006 (Feature Column, Amer. Math. Soc., http://www.ams.org/featurecolumn/archive/lorenz.html)

[Got74] Goto, Morikuni An introduction to topological groups, Lect. Notes Series, 40, Matematisk Institut, Aarhus Universitet, Aarhus, 1974 (Lectures 1973/74)

[Gro84] Gromov, M. Infinite groups as geometric objects, Proceedings of the International Congress of Mathematicians, (Warsaw, 1983), PWN, Warsaw, 1984, pp. 385-392 | Zbl

[Gro93] Gromov, M. Asymptotic invariants of infinite groups, Geometric group theory, Vol. 2 (Sussex, 1991) (London Math. Soc. Lect. Note Series), Volume 182, Cambridge Univ. Press, Cambridge, 1993, pp. 1-295 | MR

[Hat96] Hattori, Toshiaki Asymptotic geometry of arithmetic quotients of symmetric spaces, Math. Z., Volume 222 (1996) no. 2, pp. 247-277 | DOI | MR | Zbl

[Hed36] Hedlund, Gustav A. Fuchsian groups and transitive horocycles, Duke Math. J., Volume 2 (1936) no. 3, pp. 530-542 | DOI | MR | Zbl

[HW79] Hardy, G. H.; Wright, E. M. An introduction to the theory of numbers, The Clarendon Press Oxford University Press, New York, 1979 (Trad. française : Vuibert, Paris, 2007)

[Ita63] Itard, Jean Arithmétique et théorie des nombres, Que sais-je ?, 1093, Presses Universitaires de France, Paris, 1963 | MR

[Kat92] Katok, Svetlana Fuchsian groups, Chicago Lectures in Math., University of Chicago Press, Chicago, IL, 1992

[Khi97] Khinchin, A. Ya. Continued fractions, Dover Publications Inc., Mineola, NY, 1997 | MR

[LS01] Lyndon, Roger C.; Schupp, Paul E. Combinatorial group theory, Classics in Math., Springer-Verlag, Berlin, 2001 | DOI

[Mar87] Margulis, G. A. Formes quadratriques indéfinies et flots unipotents sur les espaces homogènes, C. R. Acad. Sci. Paris Sér. I Math., Volume 304 (1987) no. 10, pp. 249-253 | Zbl

[Mar89] Margulis, G. A. Indefinite quadratic forms and unipotent flows on homogeneous spaces, Dynamical systems and ergodic theory (Warsaw, 1986) (Banach Center Publ.), Volume 23, PWN, Warsaw, 1989, pp. 399-409 | Zbl

[Mar91] Margulis, G. A. Discrete subgroups of semisimple Lie groups, Ergeb. Math. Grenzgeb. (3), 17, Springer-Verlag, Berlin, 1991 | MR | Zbl

[Mar97] Margulis, G. A. Oppenheim conjecture, Fields Medallists’ lectures (World Sci. Ser. 20th Century Math.), Volume 5, World Sci. Publ., River Edge, NJ, 1997, pp. 272-327 | DOI | MR

[Mar00] Margulis, G. A. Problems and conjectures in rigidity theory, Mathematics : frontiers and perspectives, American Mathematical Society, Providence, RI, 2000, pp. 161-174 | Zbl

[Mil71] Milnor, John Introduction to algebraic $K$-theory, Annals of Math. Studies, 72, Princeton University Press, Princeton, NJ, 1971

[Opp31] Oppenheim, A. The minima of indefinite quaternary quadratic forms, Ann. of Math. (2), Volume 32 (1931) no. 2, pp. 271-298 | DOI | MR | Zbl

[Opp53] Oppenheim, A. Values of quadratic forms. I, Quart. J. Math. Oxford Ser. (2), Volume 4 (1953), pp. 54-59 | DOI | MR

[Pan95] Pansu, Pierre Sous-groupes discrets des groupes de Lie : rigidité, arithméticité, Séminaire Bourbaki, Vol. 1993/94 (Astérisque), Volume 227, Société Mathématique de France, Paris, 1995, pp. 69-105 (Exp. no. 778) | MR | Zbl

[Pau] Paulin, Frédéric De la géométrie et de la dynamique de ${\mathrm{SL}}_nℝ$ et ${\mathrm{SL}}_n\mathbb{Z}$, Systèmes dynamiques, groupes de matrices et applications arithmétiques (Journées X-UPS), Les Éditions de l’École polytechnique, Palaiseau, 2007 (ce volume) | DOI

[PH79] Pourezza, Ibrahim; Hubbard, John The space of closed subgroups of ${ℝ}^2$, Topology, Volume 18 (1979) no. 2, pp. 143-146 | DOI | MR | Zbl

[PV00] Pollington, Andrew D.; Velani, Sanju L. On a problem in simultaneous Diophantine approximation : Littlewood’s conjecture, Acta Math., Volume 185 (2000) no. 2, pp. 287-306 | DOI | MR | Zbl

[Rag72] Raghunathan, M. S. Discrete subgroups of Lie groups, Ergeb. Math. Grenzgeb. (3), 68, Springer-Verlag, New York, 1972 | MR | Zbl

[Rat91] Ratner, Marina On Raghunathan’s measure conjecture, Ann. of Math. (2), Volume 134 (1991) no. 3, pp. 545-607 | DOI | MR | Zbl

[Rat95] Ratner, Marina Interactions between ergodic theory, Lie groups, and number theory, Proceedings of the International Congress of Mathematicians, (Zürich, 1994), Birkhäuser, Basel, 1995, pp. 157-182 | DOI | MR | Zbl

[Sch] Scharein, R. KnotPlot (programme informatique, http://knotplot.com)

[Ser77] Serre, Jean-Pierre Cours d’arithmétique, Collection SUP : Le Mathématicien, 2, Presses Universitaires de France, Paris, 1977, 188 pages

[TV01] Troessaert, Gérald; Valette, Alain On values at integer points of some irrational, binary quadratic forms, Essays on geometry and related topics (Monogr. Enseign. Math.), Volume 38, Enseignement Math., Genève, 2001, pp. 597-610 | MR | Zbl

[Wei] Weisstein, E. Trefoil Knot (From MathWorld–A Wolfram Web Resource, http://mathworld.wolfram.com/TrefoilKnot.html)