Journal of Modern Dynamics (JMD)

Escape of mass in homogeneous dynamics in positive characteristic
Pages: 369 - 407, Volume 11, 2017

doi:10.3934/jmd.2017015      Abstract        References        Full text (1611.2K)           Related Articles

Alexander Kemarsky - Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark (email)
Frédéric Paulin - Laboratoire de mathématiques d’Orsay, UMR 8628 Université Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay Cedex, France (email)
Uri Shapira - Mathematics Department, Technion, Israel Institute of Technology, Haifa, 32000, Israel (email)

1 M. Aka and U. Shapira, On the evolution of continued fraction expansions in a fixed quadratic field, preprint, arXiv:1201.1280, to appear in Journal d'Analyse Mathématique.
2 J. Athreya, A. Ghosh and A. Prasad, Ultrametric logarithm laws, II, Monatsh. Math., 167 (2012), 333-356.       
3 Y. Benoist and H. Oh, Equidistribution of rational matrices in their conjugacy classes, Geom. Funct. Anal., 17 (2007), 1-32.       
4 Y. Benoist and J.-F. Quint, Random walks on finite volume homogeneous spaces, Invent. Math., 187 (2012), 37-59.       
5 E. Breuillard, Equidistribution des orbites toriques sur les espaces homogènes (d'après M. Einsiedler, E. Lindenstrauss, Ph. Michel, A. Venkatesh), Séminaire Bourbaki, Exp. 1008, Astérisque, 332 (2010), 305-339.       
6 A. Broise-Alamichel and F. Paulin, Dynamique sur le rayon modulaire et fractions continues en caractéristique p, J. London Math. Soc., 76 (2007), 399-418.       
7 L. Clozel, H. Oh and E. Ullmo, Hecke operators and equidistribution of Hecke points, Invent. Math., 144 (2001), 327-351.       
8 L. Clozel and E. Ullmo, Equidistribution des points de Hecke, in Contribution to Automorphic Forms, Geometry and Number Theory (eds. H. Hida, D. Ramakrishnan and F. Shahidi), Johns Hopkins Univ. Press, 2004, 193-254.       
9 S. G. Dani and G. Margulis, Limit distribution of orbits of unipotent flows and values of quadratic forms, Adv. Soviet Math., 16 (1993), 91-137.       
10 B. de Mathan and O. Teulié, Problèmes diophantiens simultanés, Monatsh. Math., 143 (2004), 229-245.       
11 A. Eskin and G. Margulis, Recurrence properties of random walks on finite volume homogeneous manifolds, in Random Walks and Geometry, Walter de Gruiter, Berlin, 2004, 431-444.       
12 A. Eskin and M. Mirzakani, Counting closed geodesics in moduli space, J. Mod. Dyn., 5 (2011), 71-105.       
13 A. Eskin and H. Oh, Ergodic theoretic proof of equidistribution of Hecke points, Ergodic Theory Dynam. Systems, 26 (2006), 163-167.       
14 H. Freudenthal, Über die Enden topologischer Räume und Gruppen, Math. Z., 33 (1931), 692-713.       
15 U. Hamenstädt, Dynamics of the Teichmüller flow on compact invariant sets, J. Mod. Dynamics, 4 (2010), 393-418.       
16 A. Lasjaunias, A survey of Diophantine approximation in fields of power series, Monatsh. Math., 130 (2000), 211-229.       
17 A. Lubotzky, Lattices in rank one Lie groups over local fields, Geom. Funct. Anal., 1 (1991), 406-431.       
18 H. Nagao, On $\GL(2,K[x])$, J. Inst. Polytech. Osaka City Univ. Ser. A, 10 (1959), 117-121.       
19 F. Paulin, Groupe modulaire, fractions continues et approximation diophantienne en caractéristique $p$, Geom. Dedicata., 95 (2002), 65-85.       
20 F. Paulin and U. Shapira, High degree continued fraction expansions of quadratic irrationals in positive characteristic, in preparation.
21 G. Prasad and A. Rapinchuk, Subnormal subgroups of the groups of rational points of reductive algebraic groups, Proc. Amer. Math. Soc., 130 (2002), 2219-2227.       
22 I. Reiner, Maximal Orders, London Mathematical Society Monographs, No. 5, Academic Press, London-New York, 1975.       
23 M. Rosen, Number Theory in Function Fields, Graduate Texts in Mathematics, 210, Springer-Verlag, New York, 2002.       
24 P. Sarnak, Reciprocal geodesics, Clay Math. Proc., 7 (2007), 217-237.       
25 W. Schmidt, On continued fractions and Diophantine approximation in power series fields, Acta Arith., 95 (2000), 139-166.       
26 J.-P. Serre, Local Fields, Graduate Texts in Mathematics, 67, Springer-Verlag, New York-Berlin, 1979.       
27 J.-P. Serre, Arbres, amalgames, $SL_2$, 3ème éd. corr., Astérisque, 46, Soc. Math. France, Paris, 1977.       
28 U. Shapira, Full escape of mass for the diagonal group, preprint, arXiv:1511.07251, to appear in International Mathematics Research Notices.
29 J. Tits, Classification of algebraic semisimple groups, in Algebraic Groups and Discontinuous Subgroups (Boulder, 1965), Proc. Symp. Pure Math. IX, Amer. Math. Soc., 1966, 33-62.       
30 J. Tits, Reductive groups over local fields, in Automorphic Forms, Representations and $L$-Functions (Corvallis, 1977), Part 1, Proc. Symp. Pure Math. XXXIII, Amer. Math. Soc., 1979, 29-69.       
31 A. Weil, On the analogue of the modular group in characteristic $p$, in Functional Analysis and Related Fields (Chicago, 1968), Springer, 1970, 211-223.       
32 D. Witte Morris, Ratner's Theorems on Unipotent Flows, Chicago Univ. Press, Chicago, IL, 2005.       

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