Closed orbits in homology classes
Katsuda, Atsushi ; Sunada, Toshikazu
Publications Mathématiques de l'IHÉS, Tome 72 (1990), p. 5-32 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{PMIHES_1990__71__5_0,
     author = {Katsuda, Atsushi and Sunada, Toshikazu},
     title = {Closed orbits in homology classes},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     volume = {72},
     year = {1990},
     pages = {5-32},
     mrnumber = {92m:58102},
     zbl = {0728.58026},
     language = {en},
     url = {http://dml.mathdoc.fr/item/PMIHES_1990__71__5_0}
}

Katsuda, Atsushi; Sunada, Toshikazu. Closed orbits in homology classes. Publications Mathématiques de l'IHÉS, Tome 72 (1990) pp. 5-32. http://gdmltest.u-ga.fr/item/PMIHES_1990__71__5_0/

[1] T. Adachi, Meromorphic extension of L-functions of Anosov flows and profinite graphs, Kumamoto J. Math., 1 (1988), 9-24. | MR 951819 | MR 89j:58105 | Zbl 0668.58041

[2] T. Adachi and T. Sunada, Homology of closed geodesics in a negatively curved manifold, J. Diff. Geom., 26 (1987), 81-99. | MR 892032 | MR 88g:58149 | Zbl 0618.58028

[3] T. Adachi and T. Sunada, Twisted Perron-Frobenius theorem and L-functions, J. Funct. Anal., 71 (1987), 1-46. | MR 879699 | MR 88j:58101 | Zbl 0658.58034

[4] R. Bowen, Symbolic dynamics for hyperbolic flows, Amer. J. Math., 95 (1973), 429-459. | MR 339281 | MR 49 #4041 | Zbl 0282.58009

[5] M. Denker and W. Philipp, Approximation by Brownian motion for Gibbs measures and flows under a function, Ergod. Th. & Dynam. Syst., 4 (1984), 541-552. | MR 779712 | MR 86g:28025 | Zbl 0554.60077

[6] C. Epstein, Asymptotics for closed geodesics in a homology class-finite volume case-, Duke Math. J., 55 (1987), 717-757. | MR 916117 | MR 89c:58098 | Zbl 0648.58041

[7] I. M. Gel'Fand and I. I. Pyateckii-Shapiro, A theorem of Poincaré, Dokl. Akad. Nauk., 127 (1959), 490-493 (Russian). | MR 107738 | MR 21 #6460 | Zbl 0107.17101

[8] V. Guillemin and D. Kazhdan, Some inverse spectral results for negatively curved 2-manifolds, Topology, 11 (1980), 301-312. | MR 579579 | MR 81j:58082 | Zbl 0465.58027

[9] P. H. Halmos, Measure Theory, New York, Van Nostrand Co. Inc., 1950. | MR 33869 | MR 11,504d | Zbl 0040.16802

[10] A. Katsuda, Density theorem for closed orbits, Proc. of Taniguchi Symp., Springer Lect. Notes in Math., vol. 1339, 1988, to appear. | MR 89j:58066 | Zbl 0668.58043

[11] A. Katsuda and T. Sunada, Homology and closed geodesics in a compact Riemann surface, Amer. J. Math., 110 (1988), 145-156. | MR 89e:58093 | Zbl 0647.53036

[12] S. Lang, Algebraic Number Theory, London, Addison-Wisley, 1970. | MR 44 #181 | Zbl 0211.38404

[13] A. N. Livcic, Some homological properties of U-systems, Math. Zametki, 10 (1971), 555-564.

[14] S. Manabe and Y. Ochi, The central limit theorem for current-valued processes induced by geodesic flows, Osaka J. Math., 26 (1989), 191-205. | MR 90f:58140 | Zbl 0703.60019

[15] W. Parry, Bowen's equidistribution theory and the Dirichlet density theorem, Ergod. Th. & Dynam. Syst., 4 (1984), 117-134. | MR 86j:58125 | Zbl 0567.58014

[16] W. Parry and M. Pollicott, An analogue of the prime number theorem for closed orbits of Axiom A flows, Ann. of Math., 118 (1983), 573-591. | MR 85i:58105 | Zbl 0537.58038

[17] W. Parry and M. Pollicott, The Chebotarev theorem for Galois coverings of Axiom A flows, Ergod. Th. & Dynam. Syst., 6 (1986), 133-148. | MR 88k:58124 | Zbl 0626.58006

[18] R. Phillips and P. Sarnak, Geodesics in homology classes, Duke Math. J., 55 (1987), 287-297. | MR 88g:58151 | Zbl 0642.53050

[19] J. Plante, Anosov flows, Amer. J. Math., 94 (1972), 729-758. | MR 51 #14099 | Zbl 0257.58007

[20] J. Plante, Homology of closed orbits of Axiom A flows, Proc. A. M. S., 37 (1973), 297-300. | MR 46 #10025 | Zbl 0249.58012

[21] M. Pollicott, On the rate of mixing of Axiom A flows, Invent. Math., 81 (1985), 413-426. | MR 87i:58148 | Zbl 0591.58025

[22] D. Ruelle, Thermodynamic Formalism, London, Addison-Wisley, 1978. | MR 80g:82017

[23] A. Selberg, Harmonic analysis and discontinuous subgroups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc., 20 (1956), 47-87. | MR 19,531g | Zbl 0072.08201

[24] J.-P. Serre, Divisibilité de certaines fonctions arithmétiques, L'Ens. Math., 22 (1976), 227-260. | MR 55 #7958 | Zbl 0355.10021

[25] S. Zelditch, Geodesics in homology classes and periods of automorphic forms, preprint, Johns Hopkins Univ., 1986.

[26] M. H. Delange, Généralisation du théorème de Ikehara, Ann. Scient. Ec. Norm. Sup., Sér. 3, 71 (1954), 213-242. | Numdam | MR 16,921e | Zbl 0056.33101