Distribution of closed geodesics on the modular surface and quadratic irrationals
Bulletin de la Société Mathématique de France, Tome 114 (1986), pp. 431-446. 
@article{BSMF_1986__114__431_0,
     author = {Pollicott, Mark},
     title = {Distribution of closed geodesics on the modular surface and quadratic irrationals},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {431--446},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {114},
     year = {1986},
     doi = {10.24033/bsmf.2064},
     mrnumber = {88j:58102},
     zbl = {0624.58019},
     language = {en},
     url = {http://www.numdam.org/articles/10.24033/bsmf.2064/}
}
TY  - JOUR
AU  - Pollicott, Mark
TI  - Distribution of closed geodesics on the modular surface and quadratic irrationals
JO  - Bulletin de la Société Mathématique de France
PY  - 1986
SP  - 431
EP  - 446
VL  - 114
PB  - Société mathématique de France
UR  - http://www.numdam.org/articles/10.24033/bsmf.2064/
DO  - 10.24033/bsmf.2064
LA  - en
ID  - BSMF_1986__114__431_0
ER  - 
%0 Journal Article
%A Pollicott, Mark
%T Distribution of closed geodesics on the modular surface and quadratic irrationals
%J Bulletin de la Société Mathématique de France
%D 1986
%P 431-446
%V 114
%I Société mathématique de France
%U http://www.numdam.org/articles/10.24033/bsmf.2064/
%R 10.24033/bsmf.2064
%G en
%F BSMF_1986__114__431_0
Pollicott, Mark. Distribution of closed geodesics on the modular surface and quadratic irrationals. Bulletin de la Société Mathématique de France, Tome 114 (1986), pp. 431-446. doi : 10.24033/bsmf.2064. http://www.numdam.org/articles/10.24033/bsmf.2064/

[1] Adler (R.) and Flatto (L.). - Cross section maps for geodesic flows, I, in Ergodic Theory and Dynamical Systems II, KATOK (A.) Ed., Birkhäuser, Stuttgart, 1982. | MR | Zbl

[2] Arnold (V. I.) and Avez (A.). - Ergodic problems of classical mechanics, Benjamin, New York, 1968. | MR | Zbl

[3] Billingsley (P.). - Ergodic theory and information, Wiley, New York, 1965. | MR | Zbl

[4] Bowen (R.). - The equidistribution of closed geodesics, Amer. J. Math., Vol. 94, 1972, pp. 413-423. | MR | Zbl

[5] Davenport (H.). - Multiplicative number theory, G.T.M., 74, Springer, New York, 1980. | MR | Zbl

[6] Davenport (H.) and Schmidt (W. M.). - Approximation to real numbers by quadratic irrationals, Acta Arith., Vol. 14, 1967, p. 209-223. | MR

[7] Dickson (L. E.). - History of the theory of numbers II, Chelsea, New York, 1971.

[8] Gunning (R. C.). - Lectures on modular forms, P.U.P., Princeton, 1962. | MR | Zbl

[9] Hardy (G. H.) and Wright (E. M.). - An introduction to the theory of numbers, O.U.P., Oxford, 1983. | JFM | Zbl

[10] Mayer (D. H.). - On a zeta function related to the continued fraction transformation, Bull. Soc. Math. Fr., T. 104, 1976, pp. 195-203. | Numdam | MR | Zbl

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

[12] Parry (W.) and Pollicott (M.). - An analogue of the prime number theorem for closed orbits of Axiom A flows, Annals of Math., Vol. 118, 1983, pp. 573-591. | MR | Zbl

[13] Parthasarathy (K. R.). - Introduction to probability and measure, MacMillan, India, 1980. | Zbl

[14] Pollicott (M.). - A complex Ruelle-Perron-Frobenius theorem and two counter-examples, Ergod. Th. and Dynam. Sys., Vol. 4, 1984, pp. 135-146. | MR | Zbl

[15] Ruelle (D.). - Zeta functions for expanding maps and Anosov flows, Invent. Math., Vol. 34, 1976, pp. 231-242. | MR | Zbl

[16] Ruelle (D.). - Thermodynamic Formalism, Addison-Wesley, Mass., 1978. | MR | Zbl

[17] Sarnak (P.). - Class numbers of indefinite binary quadratic forms, J. Number Theory, Vol. 15, 1982, pp. 229-247. | MR | Zbl

[18] Series (C.). - The modular surface and continued fractions, J. London Math. Soc. (to appear). | Zbl

[19] Series (C.). - On coding geodesics with continued fractions, Enseignement Mathématique, Vol. 29, Univ. de Genève, 1980, pp. 67-76. | MR | Zbl

[20] Serre (J.-P.). - A course in arithmetic, G.T.M., 7, Springer, Berlin, 1973. | MR | Zbl

[21] Titchmarsh (E. C.). - The theory of functions, O.U.P., Oxford, 1983. | Zbl

[22] Walters (P.). - Invariant measures and equilibrium states for some mappings which expand distances, Trans. Amer. Math. Soc., Vol. 236, 1978, pp. 212-153. | MR | Zbl

[23] Wiener (N.). - The Fourier integral and certain of its applications, C.U.P., Cambridge, 1933. | JFM | Zbl

Cité par Sources :