Skip to main content
Log in

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. T. Adachi, Meromorphic extension of L-functions of Anosov flows and profinite graphs,Kumamoto J. Math.,1 (1988), 9–24.

    MATH  Google Scholar 

  2. T. Adachi andT. Sunada, Homology of closed geodesics in a negatively curved manifold,J. Diff. Geom.,26 (1987), 81–99.

    MATH  Google Scholar 

  3. T. Adachi andT. Sunada, Twisted Perron-Frobenius theorem and L-functions,J. Funct. Anal.,71 (1987), 1–46.

    Article  MATH  Google Scholar 

  4. R. Bowen, Symbolic dynamics for hyperbolic flows,Amer. J. Math.,95 (1973), 429–459.

    Article  MATH  Google Scholar 

  5. M. Denker andW. Philipp, Approximation by Brownian motion for Gibbs measures and flows under a function,Ergod. Th. & Dynam. Syst.,4 (1984), 541–552.

    MATH  Google Scholar 

  6. C. Epstein, Asymptotics for closed geodesics in a homology class—finite volume case—,Duke Math. J.,55 (1987), 717–757.

    Article  MATH  Google Scholar 

  7. I. M. Gel’fand andI. I. Pyateckii-Shapiro, A theorem of Poincaré,Dokl. Akad. Nauk.,127 (1959), 490–493 (Russian).

    MATH  Google Scholar 

  8. V. Guillemin andD. Kazhdan, Some inverse spectral results for negatively curved 2-manifolds,Topology,11 (1980), 301–312.

    Article  Google Scholar 

  9. P. H. Halmos,Measure Theory, New York, Van Nostrand Co. Inc., 1950.

    MATH  Google Scholar 

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

  11. A. Katsuda andT. Sunada, Homology and closed geodesics in a compact Riemann surface,Amer. J. Math.,110 (1988), 145–156.

    Article  MATH  Google Scholar 

  12. S. Lang,Algebraic Number Theory, London, Addison-Wisley, 1970.

    MATH  Google Scholar 

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

    Google Scholar 

  14. S. Manabe andY. Ochi, The central limit theorem for current-valued processes induced by geodesic flows,Osaka J. Math.,26 (1989), 191–205.

    MATH  Google Scholar 

  15. W. Parry, Bowen’s equidistribution theory and the Dirichlet density theorem,Ergod. Th. & Dynam. Syst.,4 (1984), 117–134.

    MATH  Google Scholar 

  16. W. Parry andM. Pollicott, An analogue of the prime number theorem for closed orbits of Axiom A flows,Ann. of Math.,118 (1983), 573–591.

    Article  Google Scholar 

  17. W. Parry andM. Pollicott, The Chebotarev theorem for Galois coverings of Axiom A flows,Ergod. Th. & Dynam. Syst.,6 (1986), 133–148.

    MATH  Google Scholar 

  18. R. Phillips andP. Sarnak, Geodesics in homology classes,Duke Math. J.,55 (1987), 287–297.

    Article  MATH  Google Scholar 

  19. J. Plante, Anosov flows,Amer. J. Math.,94 (1972), 729–758.

    Article  MATH  Google Scholar 

  20. J. Plante, Homology of closed orbits of Axiom A flows,Proc. A. M. S.,37 (1973), 297–300.

    Article  MATH  Google Scholar 

  21. M. Pollicott, On the rate of mixing of Axiom A flows,Invent. Math.,81 (1985), 413–426.

    Article  MATH  Google Scholar 

  22. D. Ruelle,Thermodynamic Formalism, London, Addison-Wisley, 1978.

    MATH  Google Scholar 

  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.

    Google Scholar 

  24. J.-P. Serre, Divisibilité de certaines fonctions arithmétiques,L’Ens. Math.,22 (1976), 227–260.

    MATH  Google Scholar 

  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.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Dedicated to Pr. Akihiko Morimoto for his 60th birthday

About this article

Cite this article

Katsuda, A., Sunada, T. Closed orbits in homology classes. Publications Mathématiques de L’Institut des Hautes Scientifiques 71, 5–32 (1990). https://doi.org/10.1007/BF02699875

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02699875

Keywords

Navigation