Geodesic excursions into an embedded disc on a hyperbolic Riemann surface
HTML articles powered by AMS MathViewer
- by Andrew Haas
- Conform. Geom. Dyn. 13 (2009), 1-5
- DOI: https://doi.org/10.1090/S1088-4173-09-00185-4
- Published electronically: February 3, 2009
- PDF | Request permission
Abstract:
We calculate the asymptotic average rate at which a generic geodesic on a finite area hyperbolic $2$-orbifold returns to an embedded disc on the surface, as well as the average amount of time it spends in the disc during each visit. This includes the case where the center of the disc is a cone point.References
- Alan F. Beardon, The geometry of discrete groups, Graduate Texts in Mathematics, vol. 91, Springer-Verlag, New York, 1983. MR 698777, DOI 10.1007/978-1-4612-1146-4
- Tim Bedford, Michael Keane, and Caroline Series (eds.), Ergodic theory, symbolic dynamics, and hyperbolic spaces, Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1991. Papers from the Workshop on Hyperbolic Geometry and Ergodic Theory held in Trieste, April 17–28, 1989. MR 1130170
- I. P. Cornfeld, S. V. Fomin, and Ya. G. Sinaĭ, Ergodic theory, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 245, Springer-Verlag, New York, 1982. Translated from the Russian by A. B. Sosinskiĭ. MR 832433, DOI 10.1007/978-1-4615-6927-5
- Andrew Haas, The distribution of geodesic excursions into the neighborhood of a cone singularity on a hyperbolic 2-orbifold, Comment. Math. Helv. 83 (2008), no. 1, 1–20. MR 2365405, DOI 10.4171/CMH/115
- A. Haas, Geodesic cusp excursions and metric diophantine approximation, Preprint arxiv:0709.0313. To appear in Math. Res. Letters.
- Hitoshi Nakada, On metrical theory of Diophantine approximation over imaginary quadratic field, Acta Arith. 51 (1988), no. 4, 399–403. MR 971089, DOI 10.4064/aa-51-4-393-403
- Peter J. Nicholls, The ergodic theory of discrete groups, London Mathematical Society Lecture Note Series, vol. 143, Cambridge University Press, Cambridge, 1989. MR 1041575, DOI 10.1017/CBO9780511600678
- Bernd Stratmann, A note on counting cuspidal excursions, Ann. Acad. Sci. Fenn. Ser. A I Math. 20 (1995), no. 2, 359–372. MR 1346819
Bibliographic Information
- Andrew Haas
- Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
- Email: haas@math.uconn.edu
- Received by editor(s): April 29, 2008
- Published electronically: February 3, 2009
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Conform. Geom. Dyn. 13 (2009), 1-5
- MSC (2000): Primary 30F35, 32Q45, 37E35, 53D25
- DOI: https://doi.org/10.1090/S1088-4173-09-00185-4
- MathSciNet review: 2476655