Correlations for pairs of closed geodesics

Inventiones Mathematicae

Volumn 163, Issue 1, 2006, Pages 1-24

  Pollicott, Mark ^a   Sharp, Richard ^b  

^a UNIVERSITY OF WARWICK   (United Kingdom)

^b UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 29144492861     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00222-004-0427-7     Document Type: Article

References (33)

1. Adler, R., Flatto, L.: Geodesic flows, interval maps, and symbolic dynamics. Bull. Am. Math. Soc. 25, 229-334 (1991)
2. Aurich, R., Bogomolny, E., Steiner, F.: Periodic orbits on the regular hyperbolic octagon. Physica D 48, 91-101 (1991)
3. Aurich, R., Steiner, F.: On the periodic orbits of a strongly chaotic system. Physica D 32, 451-460 (1988)
4. Berry, M.: Semiclassical theory of spectral rigidity. Proc. R. Soc. Lond. Ser. A 400, 229-251 (1985)
5. Birman, J., Series, C.: Dehn's algorithm revisited, with applications to simple curves on surfaces. In: Combinatorial group theory and topology (Alta, Utah, 1984). Ann. Math. Stud., vol. 111, pp. 451-478. Princeton, NJ: Princeton University Press 1987
6. Breiman, L.: Probability. Reading, MA: Addison-Wesley 1968
7. Buser, P.: Geometry and spectra of compact Riemann surfaces. In: Progress in Mathematics, vol. 106. Boston: Birkhauser 1992
8. Dolgopyat, D.: On decay of correlations in Anosov flows. Ann. Math. 147, 357-390 (1998)
9. Huber, H.: Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen. II. Math. Ann. 142, 385-398 (1960)
10. Katok, A.: Four applications of conformal equivalence to geometry and dynamics. Ergodic Theory Dyn. Syst. 8*, 139-152 (1988)
11. Katok, A., Hasselblatt, B.: Introduction to the modern theory of dynamical systems. In: Encyclopedia of Mathematics and its Applications, vol. 54. Cambridge: Cambridge University Press 1995
12. Katsuda, A., Sunada, T.: Closed orbits in homology classes. Publ. Math., Inst. Hautes Étud. Sci. 71, 5-32 (1990)
13. Keating, J.: Periodic orbits, spectral statistics, and the Riemann zeros. In: Supersymmetry and Trace Formulae: Chaos and Disorder, NATO ASI Series, Series B: Physics, Vol. 370, pp 1-17. New York: Kluwer 1999
14. Luo, W., Sarnak, P.: Number variance for arithmetic hyperbolic surfaces. Commun. Math. Phys. 161, 419-432 (1994)
15. Margulis, G.: Certain applications of ergodic theory to the investigation of manifolds of negative curvature. Funkts. Anal. Prilozh. 3, 89-90 (1969)
16. Marklof, J.: On multiplicities in length spectra of arithmetic hyperbolic three-orbifolds. Nonlinearity 9, 517-536 (1996)
17. Marklof, J.: Pair correlation densities of inhomogeneous quadratic forms. Ann. Math. 158, 419-471 (2003)
18. Montgomery, H.: The pair correlation of zeros of the zeta function. Proc. Symp. Pure Math. 24, 181-193 (1973)
19. Parry, W., Pollicott, M.: Zeta functions and the periodic orbit structure of hyperbolic dynamics. Astérisque 187-188, 1-268 (1990)
20. q extensions of subshifts of finite type. J. Lond. Math. Soc. 49, 401-416 (1994)
21. Postnikov, A.: Introduction to analytic number theory. In: Translations of Mathematical Monographs, Vol. 68. Providence, RI: Am. Math. Soc. 1988
22. Randol, B.: The length spectrum of a Riemann surface is always of unbounded multiplicity. Proc. Am. Math. Soc. 78, 455-456 (1980)
23. Rudnick, Z., Sarnak, P.: The n-level correlations of zeros of the zeta function. C. R. Acad. Sci., Paris, Sér. I, Math. 319, 1027-1032 (1994)
24. Rudnick, Z., Sarnak, P.: The pair correlation function of fractional parts of polynomials. Commun. Math. Phys. 194, 61-70 (1998)
25. Ruelle, D.: Thermodynamic formalism. New York: Addison-Wesley 1978
26. Ruelle, D.: An extension of the theory of Fredholm determinants. Publ. Math., Inst. Hautes Études Sci. 72, 175-193 (1990)
27. Sarnak, P.: Class numbers of indefinite binary quadratic forms. J. Number Theory 15, 229-247 (1982)
28. Series, C.: Symbolic dynamics for geodesic flows. Acta Math. 146, 103-128 (1981)
29. Series, C.: The infinite word problem and limit sets in Fuchsian groups. Ergodic Theory Dyn. Syst. 1, 337-360 (1981)
30. Series, C.: Geometrical Markov coding of geodesics on surfaces of constant negative curvature. Ergodic Theory Dyn. Syst. 6, 601-625 (1986)
31. Series, C.: Geometrical methods of symbolic coding. In: Ergodic theory, symbolic dynamics, and hyperbolic spaces (Trieste, 1989), ed. by T. Bedford, M. Keane, C. Series, pp. 125-151. Oxford: Oxford University Press 1991
32. Stephenson, G.: Mathematical methods for science students. London: Longman 1961
33. Walters, P.: An introduction to ergodic theory. In: Graduate Texts in Mathematics, vol. 79. New York, Berlin: Springer 1982