Closed orbits in homology classes
Publications Mathématiques de l'IHÉS, Tome 71 (1990), pp. 5-32 
@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},
     pages = {5--32},
     year = {1990},
     publisher = {Institut des Hautes Etudes Scientifiques},
     volume = {71},
     mrnumber = {1079641},
     zbl = {0728.58026},
     language = {en},
     url = {https://www.numdam.org/item/PMIHES_1990__71__5_0/}
}
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Katsuda, Atsushi; Sunada, Toshikazu. Closed orbits in homology classes. Publications Mathématiques de l'IHÉS, Tome 71 (1990), pp. 5-32. https://www.numdam.org/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. | Zbl | MR

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

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

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

[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. | Zbl | MR

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

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

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

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

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

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

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

[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. | Zbl | MR

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

[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. | Zbl | MR

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

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

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

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

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

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

[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. | Zbl | MR

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

[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. | Zbl | MR | Numdam