Angular self-intersections for closed geodesics on surfaces
HTML articles powered by AMS MathViewer
- by Mark Pollicott and Richard Sharp PDF
- Proc. Amer. Math. Soc. 134 (2006), 419-426 Request permission
Abstract:
In this note we consider asymptotic results for self-intersections of closed geodesics on surfaces for which the angle of the intersection occurs in a given arc. We do this by extending Bonahon’s definition of intersection forms for surfaces.References
- N. Anantharaman, Distribution of closed geodesics on a surface, under homological constraints, preprint, 1999.
- D. V. Anosov, Geodesic flows on closed Riemann manifolds with negative curvature. , Proceedings of the Steklov Institute of Mathematics, No. 90 (1967), American Mathematical Society, Providence, R.I., 1969. Translated from the Russian by S. Feder. MR 0242194
- Joan S. Birman and Caroline Series, Geodesics with bounded intersection number on surfaces are sparsely distributed, Topology 24 (1985), no. 2, 217–225. MR 793185, DOI 10.1016/0040-9383(85)90056-4
- Francis Bonahon, Bouts des variétés hyperboliques de dimension $3$, Ann. of Math. (2) 124 (1986), no. 1, 71–158 (French). MR 847953, DOI 10.2307/1971388
- Francis Bonahon, The geometry of Teichmüller space via geodesic currents, Invent. Math. 92 (1988), no. 1, 139–162. MR 931208, DOI 10.1007/BF01393996
- D. Dolgopyat, On statistical properties of geodesic flows on negatively curved surfaces, Ph.D. thesis, Princeton, 1997.
- Heinz Huber, Zur analytischen Theorie hyperbolischen Raumformen und Bewegungsgruppen, Math. Ann. 138 (1959), 1–26 (German). MR 109212, DOI 10.1007/BF01369663
- Heinz Huber, Zur analytischen Theorie hyperbolischer Raumformen und Bewegungsgruppen. II, Math. Ann. 142 (1960/61), 385–398 (German). MR 126549, DOI 10.1007/BF01451031
- J. Keating, Periodic orbits, spectral statistics, and the Riemann zeros, Supersymmetry and trace formulae (I. Lerner, J. Keating and D. Khmelnitskii, eds.), Kluwer, New York, 1999, pp. 1-15.
- Yuri Kifer, Large deviations, averaging and periodic orbits of dynamical systems, Comm. Math. Phys. 162 (1994), no. 1, 33–46. MR 1272765, DOI 10.1007/BF02105185
- Steven P. Lalley, Self-intersections of closed geodesics on a negatively curved surface: statistical regularities, Convergence in ergodic theory and probability (Columbus, OH, 1993) Ohio State Univ. Math. Res. Inst. Publ., vol. 5, de Gruyter, Berlin, 1996, pp. 263–272. MR 1412610
- G. A. Margulis, Certain applications of ergodic theory to the investigation of manifolds of negative curvature, Funkcional. Anal. i Priložen. 3 (1969), no. 4, 89–90 (Russian). MR 0257933
- Jean-Pierre Otal, Le théorème d’hyperbolisation pour les variétés fibrées de dimension 3, Astérisque 235 (1996), x+159 (French, with French summary). MR 1402300
- Mark Pollicott, Asymptotic distribution of closed geodesics, Israel J. Math. 52 (1985), no. 3, 209–224. MR 815810, DOI 10.1007/BF02786516
- Mark Pollicott and Richard Sharp, Exponential error terms for growth functions on negatively curved surfaces, Amer. J. Math. 120 (1998), no. 5, 1019–1042. MR 1646052, DOI 10.1353/ajm.1998.0041
- M. Sieber and K. Richter, Correlations between periodic orbits and their rôle in spectral statistics, Physica Scripta T90 (2001), 128-133.
Additional Information
- Mark Pollicott
- Affiliation: Department of Mathematics, Manchester University, Oxford Road, Manchester M13 9PL, United Kingdom
- Address at time of publication: Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
- MR Author ID: 140805
- Richard Sharp
- Affiliation: Department of Mathematics, Manchester University, Oxford Road, Manchester M13 9PL, United Kingdom
- MR Author ID: 317352
- Received by editor(s): October 15, 2003
- Received by editor(s) in revised form: September 4, 2004
- Published electronically: September 20, 2005
- Additional Notes: The second author was supported by an EPSRC Advanced Research Fellowship
- Communicated by: Michael Handel
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 419-426
- MSC (2000): Primary 37C27, 37D20, 37D35, 37D40
- DOI: https://doi.org/10.1090/S0002-9939-05-08382-6
- MathSciNet review: 2176010