## Comparison theorems and orbit counting in hyperbolic geometry

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- by Mark Pollicott and Richard Sharp PDF
- Trans. Amer. Math. Soc.
**350**(1998), 473-499 Request permission

## Abstract:

In this article we address an interesting problem in hyperbolic geometry. This is the problem of comparing different quantities associated to the fundamental group of a hyperbolic manifold (e.g. word length, displacement in the universal cover, etc.) asymptotically. Our method involves a mixture of ideas from both “thermodynamic” ergodic theory and the automaton associated to strongly Markov groups.## References

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## Additional Information

**Mark Pollicott**- Affiliation: Department of Mathematics, University of Warwick, Coventry, CV4 7AL, U.K.
- Address at time of publication: Department of Mathematics, University of Manchester, Oxford Road, Man- chester, M13 9PL, U.K.
- MR Author ID: 140805
- Email: mp@ma.man.ac.uk
**Richard Sharp**- Affiliation: Mathematical Institute, 24-29 St. Giles, Oxford, OX1 3LB, U.K.
- Address at time of publication: Department of Mathematics, University of Manchester, Oxford Road, Man- chester, M13 9PL, U.K.
- MR Author ID: 317352
- Email: sharp@ma.man.ac.uk
- Received by editor(s): May 23, 1995
- Additional Notes: The first author was supported by The Royal Society through a University Research Fellowship. The second author was supported by the UK SERC under grant number GR/G51930 held at Queen Mary and Westfield College.
- © Copyright 1998 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**350**(1998), 473-499 - MSC (1991): Primary 20F32, 22E40, 58E40; Secondary 11F72, 20F10, 58F20
- DOI: https://doi.org/10.1090/S0002-9947-98-01756-5
- MathSciNet review: 1376553