Precise counting results for closed orbits of Anosov flows

Annales Scientifiques de l'Ecole Normale Superieure

Volumn 33, Issue 1, 2000, Pages 33-56

  Anantharaman, Nalini ^a  

^a CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033636318     PISSN: 00129593     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-9593(00)00102-6     Document Type: Article

References (31)

1. T. Adachi And T. Sunada, Homology of closed geodesics in a negatively curved manifold, J. Differential Geom. 26 (1987) 81-99.
2. D.V. Anosov, Geodesic flows on closed Riemann manifolds with negative curvature, Proc. Stekl. Inst. of Math. 90 (1969).
3. V. Bangert, Minimal geodesics, Ergodic Theory Dynamical Systems 10 (1989) 263-286.
4. M. Babillot And F. Ledrappier, Lalley's theorem on periodic orbits of hyperbolic flows, Ergodic Theory Dynamical Systems 18 (1998) 17-39.
5. R. Bowen, Symbolic dynamics for hyperbolic flows, Amer. J. Math. 95 (1973) 429-460.
6. N. Chernov, Markov approximations and decay of correlations for Anosov flows, Ann. of Math. (to appear).
7. E.T. Copson, Asymptotic Expansions, Cambridge University Press, 1965.
8. D. Dolgopyat, On decay of correlations in Anosov flows, Ann. of Math. (to appear).
9. B. Hasselblatt, Regularity of the Anosov splitting and of horospheric foliations, Ergodic Theory Dynamical Systems 14 (1994) 645-666.
10. H. Huber, Zur analytischen theorie hyperbolischer raumformen und bewegungsgruppen (I), Math. Ann. 138 (1959) 1-26; (II), Math. Ann. 142 (1961) 385-398; (III), Math. Ann. 143 (1961) 463-464.
11. H. Huber, Zur analytischen theorie hyperbolischer raumformen und bewegungsgruppen (I), Math. Ann. 138 (1959) 1-26; (II), Math. Ann. 142 (1961) 385-398; (III), Math. Ann. 143 (1961) 463-464.
12. H. Huber, Zur analytischen theorie hyperbolischer raumformen und bewegungsgruppen (I), Math. Ann. 138 (1959) 1-26; (II), Math. Ann. 142 (1961) 385-398; (III), Math. Ann. 143 (1961) 463-464.
13. L. Hormander, The analysis of partial differential operators, A Series of Comprehensive Studies in Mathematics, Vol. 256, Springer, Berlin, 1983.
14. A. Katsuda And T. Sunada, Homology and closed geodesics in a compact Riemann surface, Amer. J. Math. 110 (1988) 145-156.
15. A. Katsuda And T. Sunada, Closed orbits in homology classes, Publ. Math. IHES 71 (1990) 5-32.
16. Y. Kifer, Large deviations, averaging and periodic orbits of dynamical systems, Comm. Math. Phys. 162 (1994) 33-46.
17. S. Lalley, Distribution of periodic orbits of symbolic and Axiom A flows, Adv. Appl. Math. 8 (1987) 154-193.
18. S. Lalley, Closed geodesics in homology classes on surfaces of variable negative curvature, Duke Math. J. 58 (1989) 795-821.
19. B. Marcus, Unique ergodicity of some flows related to Axiom A diffeomorphisms, Israel J. Math. 21 (1975) 111-132.
20. G. Margulis, Applications of ergodic theory for the investigation of manifolds of negative curvature, Funct. Anal. Appl. 3 (1969) 335-336.
21. W. Parry And M. Pollicott, Zeta functions and the periodic orbit structure of hyperbolics dynamics, Astrisque 187-188 (1990).
22. R. Phillips And P. Sarnak, Geodesics in homology classes, Duke Math. J. 55 (1987) 287-297.
23. M. Pollicott, Homology and closed geodesics in a compact negatively curved surface, Amer. J. Math. 113 (1991) 379-385.
24. M. Pollicott And R. Sharp, Error terms for growth functions on negatively curved surfaces, Amer. J. Math. (to appear).
25. M. Pollicott And R. Sharp, Asymptotic Expansions for Closed Orbits in Homology Classes, Preprint.
26. M. Ratner, Markov partitions for Anosov flows on n-dimensional manifolds, Israel J. Math. 15 (1973) 92-114.
27. R.T. Rockafellar, Convex Analysis, Princeton University Press, 1970.
28. D. Ruelle, An extension of the theory of Fredholm determinants, Publ. Math. IHES 72 (1990) 175-193.
29. S. Schwartzmann, Asymptotic cycles, Ann. of Math. 66 (1957) 270-284.
30. R. Sharp, Prime orbits theorems with multi-dimensional constraints for Axiom A flows, Mh. Math. 114 (1992) 261-304.
31. R. Sharp, Closed orbits in homology classes for Anosov flows, Ergodic Theory Dynamical Systems 13 (1993) 387-408.