Precise counting results for closed orbits of Anosov flows
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 33 (2000) no. 1, pp. 33-56. 
@article{ASENS_2000_4_33_1_33_0,
     author = {Anantharaman, Nalini},
     title = {Precise counting results for closed orbits of {Anosov} flows},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {33--56},
     publisher = {Elsevier},
     volume = {Ser. 4, 33},
     number = {1},
     year = {2000},
     doi = {10.1016/s0012-9593(00)00102-6},
     mrnumber = {2002c:37048},
     zbl = {0992.37026},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/s0012-9593(00)00102-6/}
}
TY  - JOUR
AU  - Anantharaman, Nalini
TI  - Precise counting results for closed orbits of Anosov flows
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 2000
SP  - 33
EP  - 56
VL  - 33
IS  - 1
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/s0012-9593(00)00102-6/
DO  - 10.1016/s0012-9593(00)00102-6
LA  - en
ID  - ASENS_2000_4_33_1_33_0
ER  - 
%0 Journal Article
%A Anantharaman, Nalini
%T Precise counting results for closed orbits of Anosov flows
%J Annales scientifiques de l'École Normale Supérieure
%D 2000
%P 33-56
%V 33
%N 1
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/s0012-9593(00)00102-6/
%R 10.1016/s0012-9593(00)00102-6
%G en
%F ASENS_2000_4_33_1_33_0
Anantharaman, Nalini. Precise counting results for closed orbits of Anosov flows. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 33 (2000) no. 1, pp. 33-56. doi : 10.1016/s0012-9593(00)00102-6. http://archive.numdam.org/articles/10.1016/s0012-9593(00)00102-6/

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

[2] D.V. Anosov, Geodesic flows on closed Riemann manifolds with negative curvature, Proc. Stekl. Inst. of Math. 90 (1969). | MR | Zbl

[3] V. Bangert, Minimal geodesics, Ergodic Theory Dynamical Systems 10 (1989) 263-286. | MR | Zbl

[4] M. Babillot and F. Ledrappier, Lalley's theorem on periodic orbits of hyperbolic flows, Ergodic Theory Dynamical Systems 18 (1998) 17-39. | MR | Zbl

[5] R. Bowen, Symbolic dynamics for hyperbolic flows, Amer. J. Math. 95 (1973) 429-460. | MR | Zbl

[6] N. Chernov, Markov approximations and decay of correlations for Anosov flows, Ann. of Math. (to appear). | Zbl

[7] E.T. Copson, Asymptotic Expansions, Cambridge University Press, 1965. | MR | Zbl

[8] D. Dolgopyat, On decay of correlations in Anosov flows, Ann. of Math. (to appear). | Zbl

[9] B. Hasselblatt, Regularity of the Anosov splitting and of horospheric foliations, Ergodic Theory Dynamical Systems 14 (1994) 645-666. | MR | Zbl

[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. | MR | Zbl

[11] L. Hormander, The Analysis of Partial Differential Operators, A series of comprehensive studies in mathematics, Vol. 256, Springer, Berlin, 1983. | MR | Zbl

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

[13] A. Katsuda and T. Sunada, Closed orbits in homology classes, Publ. Math. IHES 71 (1990) 5-32. | Numdam | MR | Zbl

[14] Y. Kifer, Large deviations, averaging and periodic orbits of dynamical systems, Comm. Math. Phys. 162 (1994) 33-46. | MR | Zbl

[15] S. Lalley, Distribution of periodic orbits of symbolic and Axiom A flows, Adv. Appl. Math. 8 (1987) 154-193. | MR | Zbl

[16] S. Lalley, Closed geodesics in homology classes on surfaces of variable negative curvature, Duke Math. J. 58 (1989) 795-821. | MR | Zbl

[17] B. Marcus, Unique ergodicity of some flows related to Axiom A diffeomorphisms, Israel J. Math. 21 (1975) 111-132. | MR | Zbl

[18] G. Margulis, Applications of ergodic theory for the investigation of manifolds of negative curvature, Funct. Anal. Appl. 3 (1969) 335-336. | MR | Zbl

[19] W. Parry and M. Pollicott, Zeta functions and the periodic orbit structure of hyperbolics dynamics, Astrisque 187-188 (1990). | Numdam | MR | Zbl

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

[21] M. Pollicott, Homology and closed geodesics in a compact negatively curved surface, Amer. J. Math. 113 (1991) 379-385. | MR | Zbl

[22] M. Pollicott and R. Sharp, Error terms for growth functions on negatively curved surfaces, Amer. J. Math. (to appear).

[23] M. Pollicott and R. Sharp, Asymptotic expansions for closed orbits in homology classes, Preprint.

[24] M. Ratner, Markov partitions for Anosov flows on n-dimensional manifolds, Israel J. Math. 15 (1973) 92-114. | MR | Zbl

[25] R.T. Rockafellar, Convex Analysis, Princeton University Press, 1970. | MR | Zbl

[26] D. Ruelle, An extension of the theory of Fredholm determinants, Publ. Math. IHES 72 (1990) 175-193. | Numdam | MR | Zbl

[27] S. Schwartzmann, Asymptotic cycles, Ann. of Math. 66 (1957) 270-284. | MR | Zbl

[28] R. Sharp, Prime orbits theorems with multi-dimensional constraints for Axiom A flows, Mh. Math. 114 (1992) 261-304. | MR | Zbl

[29] R. Sharp, Closed orbits in homology classes for Anosov flows, Ergodic Theory Dynamical Systems 13 (1993) 387-408. | MR | Zbl

Cité par Sources :