# Comparison theorems and orbit counting in hyperbolic geometry

@article{Pollicott1998ComparisonTA, title={Comparison theorems and orbit counting in hyperbolic geometry}, author={Mark Pollicott and Richard Sharp}, journal={Transactions of the American Mathematical Society}, year={1998}, volume={350}, pages={473-499} }

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 tnixture of ideas from both "thermodynamic" ergodic theory and the automaton associated to strongly Markov groups. 0. INTRODUCTION In [5] Cannon showed that for fundamental groups of many manifolds of negative… Expand

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