Lalley's theorem on periodic orbits of hyperbolic flows

Ergodic Theory and Dynamical Systems

Volumn 18, Issue 1, 1998, Pages 17-39

  Babillot, Martine ^a   Ledrappier, François ^b  

^a University of Paris VII LPSM partially supported by ERC Starting Grant 680275 MALIG   (France)

^b ECOLE POLYTECHNIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040350233     PISSN: 01433857     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0143385798100330     Document Type: Article

References (33)

1. T. Adachi and T. Sunada. Homology of closed geodesics in a negatively curved manifold. J. Diff. Geom. 26 (1987), 81-99.
2. M. Babillot. Théorie du renouvellement pour des chaînes semi-markoviennes transientes. Annales Inst. H. Poincaré 24(4) (1988), 507-569.
3. L. Breiman. Probability. Addison-Wesley, 1968.
4. R. Bowen. The equidistribution of closed geodesics. Amer. J. Math. 94 (1972), 413-423.
5. R. Bowen. Symbolic dynamics for hyperbolic flows. Amer. J. Math. 95 (1973), 429-460.
6. R. Bowen and D. Ruelle. The ergodic theory of Axiom A flows. Inventiones Math. 29 (1975), 181-202.
7. M. Denker, C. Grillenberger and K. Sigmund. Ergodic Theory on Compact Spaces (Springer Lecture Notes in Mathematics, 527), 1976.
8. F. Dal'bo and M. Peigné. Dénombrement des géodésiques fermées de la surface modulaire en courbure non constante. In 'Méthode des opérateurs de transfert: transformations dilatantes de l'intervalle et dénombrement de géodesiques fermées', Astérisque 238. Soc. Math. France, 1997.
9. F. Dal'bo and M. Peigné. Groupes de ping-pong et géodésiques fermées en courbure -1. Annales Inst. Fourier 46 (1996), 755-799.
10. F. Dal'bo and M. Peigné. Counting closed geodesics on locally CAT(-1)-spaces with cusps. Preprint Universiteé de Rennes I, 1996. To appear in J. Reine Angew. Math. (1998).
11. A. Eskin and C. McMullen. Mixing, counting and equidistribution in Lie groups. Duke Math. J. 71 (1993), 181-209.
12. C. Epstein. Asymptotics for closed geodesics in a homology class-finite volume case. Duke. Math. J. 55 (1987), 717-757.
13. D. Fried. The geometry of cross sections to flows. Topology 21 (1982), 353-371.
14. N. T. A. Haydn. Meromorphic extensions of the zeta function for Axiom A flows. Ergod. Th. & Dynam. Sys. 10 (1990), 347-360.
15. L. Hörmander. The Analysis of Partial Differential Operators I (A Series of Comprehensive Studies in Mathematics, 256). Springer, 1983.
16. Y. Kifer. Large deviations, averaging and periodic orbits of dynamical systems. Comm. Math. Phys. 162 (1994), 33-46.
17. A Katsuda and T. Sunada. Closed orbits in homology classes. Publ. Math. IHES 71 (1990), 5-32.
18. S. Lalley. Distribution of periodic orbits of symbolic and Axiom A flows. Adv. Appl. Math. 8 (1987), 154-193.
19. S. Lalley. Renewal theorems in symbolic dynamics with applications to geodesic flows, non euclidean tesselations and their fractal limits. Acta. Math. 163 (1989), 1-55.
20. S. Lalley. Closed geodesics in homology classes on surfaces of variable negative curvature. Duke Math. J. 58 (1989), 795-821.
21. F. Ledrappier. A renewal theorem for the distance in negative curvature. Proc. Symp. Pure Math. 57 (1995), 351-360.
22. G. A. Margulis. Applications of ergodic theory to the investigation of manifolds of negative curvature. Func. Anal. Appl. 3 (1969), 335-336.
23. M. Pollicott. Homology and closed geodesics in a compact negatively curved surface. Amer. J. Math. 113 (1991), 379-385.
24. W. Parry and M. Pollicott. The Chebotarev theorem for Galois coverings of Axiom A flows. Ergod. Th. & Dynam. Sys. 6 (1986), 133-148.
25. W. Parry and M. Pollicott. Zeta Functions and the Periodic Orbit Structure of Hyperbolic Dynamics. Astérisque 187-188, 1990.
26. R. Phillips and P. Sarnak. Geodesics in homology classes. Duke Math. J. 55 (1987), 287-297.
27. M. Ratner. The central limit theorem for geodesic flows on n-dimensional manifolds of negative curvature. Israel J. Math. 16 (1973), 181-193.
28. R. T. Rockafellar. Convex Analysis. Princeton University Press, 1970.
29. D. Ruelle. Thermodynamic Formalism. Addison-Wesley, London, 1978.
30. S. Schwartzmann. Asymptotic cycles. Ann. of Math. 66 (1957), 270-284.
31. R. Sharp. Closed orbits in homology classes for Anosov flows. Ergod. Th. & Dynam. Sys. 13 (1993), 387-408.
32. C. Stone. Applications of unsmoothing and Fourier analysis to random walks. Markov Processes and Potential Theory. Wiley, 1967.
33. 2(R) and the equidistribution theory of closed geodesics. Duke. Math. J. 59 (1989), 27-81.