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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.
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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