# Rational ergodicity of geodesic flows

```@inproceedings{Aaronson2007RationalEO,
title={Rational ergodicity of geodesic flows},
author={Jon Aaronson and D. Sullivan},
year={2007}
}```
• Published 2007
We prove the rational egodicity of geodesic flows on divergence type surfaces of constant negative curvature, and identify their asymptotic types. 0. Introduction We discuss recurrence and transitivity properties of geodesies on hyperbolic surfaces (complete, two dimensional Riemannian manifolds with constant curvature -1). Every such surface has the unit disc as universal cover and can be viewed as H/Y where H is the unit disc equipped with the hyperbolic metric and Y is the covering group of… CONTINUE READING

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#### References

##### Publications referenced by this paper.
Showing 1-10 of 17 references

BY EBERHARD HOPF
2007

## The density at infinity of a discrete group of hyperbolic motions

MATHÉMATIQUES DE L’I.H.É.S
2003

## Checking ergodicity of some geodesic flows with infinite Gibbs measure

M. Rees
Ergod. Th. & Dynam. Sys. 1 • 1981

## On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions

D. Sullivan
Annals of Math. Studies, 97 • 1979

## On the pointwise ergodic behaviour of transformations preserving infinite measures

J. Aaronson
IsraelJ. Math. 32 • 1979

W. Thurston
Preprint, • 1978

## On the ergodic theory of non-integrable functions and infinite measure spaces

J. Aaronson
Israel J. Math. 27 • 1977

## Rational ergodicity and a metric invariant for Markov shifts

J. Aaronson
IsraelJ. Math. 27 • 1977

## Transitivity properties of Fuchsian groups

P. Nicholls
Canad. J. Math. 28 • 1976