Hostname: page-component-74656f9884-j7cmm Total loading time: 0 Render date: 2026-11-10T15:39:52.725Z Has data issue: false hasContentIssue false
  • English
  • Français

Rational ergodicity of geodesic flows

Published online by Cambridge University Press:  19 September 2008

Jon Aaronson  and
Dennis Sullivan
Jon Aaronson
Affiliation:
Department of Mathematics, Tel Aviv University, Tel Aviv, Israel;
Dennis Sullivan
Affiliation:
IHES, 35 Route de Chartres, 91440 Bures-sur-Yvette, France
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

We prove the rational egodicity of geodesic flows on divergence type surfaces of constant negative curvature, and identify their asymptotic types.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 4 , Issue 2 , June 1984 , pp. 165 - 178
Copyright
Copyright © Cambridge University Press 1984

References

REFERENCES

[1]Aaronson, J.. On the ergodic theory of non-integrable functions and infinite measure spaces. Israel J. Math. 27 (1977), 163–173.CrossRefGoogle Scholar
[2]Aaronson, J.. Rational ergodicity and a metric invariant for Markov shifts. Israel J. Math. 27 (1977), 93–123.CrossRefGoogle Scholar
[3]Aaronson, J.. On the pointwise ergodic behaviour of transformations preserving infinite measures. Israel J. Math. 32 (1979), 67–82.CrossRefGoogle Scholar
[4]Ford, L. R.. Automorphic Functions. McGraw-Hill, 1929 and Chelsea, 1951.Google Scholar
[5]Hedlund, G.. The dynamics of geodesic flows. Bull Amer. Math. Soc. 45 (1939), 241–260.CrossRefGoogle Scholar
[6]Hopf, E.. Fuchsian groups and ergodic theory. Trans. Amer. Math. Soc. 39 (1936), 299–314.CrossRefGoogle Scholar
[7]Hopf, E.. Ergodentheorie. Chelsea, (1948).Google Scholar
[8]Hopf, E.. Statistik der geodätischen Linien in Mannigfaltigkeiten negativer Krümmung. Ber. Verh. Sächs. Akad. Wiss. Leipzig 91 (1939), 261–304.Google Scholar
[9]Hopf, E.. Ergodic theory and the geodesic flow. Bull. Amer. Math. Soc. 77 (1972), 863–871.CrossRefGoogle Scholar
[10]Nicholls, P.. Transitivity properties of Fuchsian groups. Canad. J. Math. 28 (1976), 805–814.CrossRefGoogle Scholar
[11]Patterson, S. J.. A lattice-point problem in hyperbolic space. Mathematika 22 (1975), 81–88.CrossRefGoogle Scholar
[12]Poincaré, H.. Oeuvres. Gauthier-Villars: Paris, 1956.Google Scholar
[13]Rees, M.. Checking ergodicity of some geodesic flows with infinite Gibbs measure. Ergod. Th. & Dynam. Sys. 1 (1981), 107–133.CrossRefGoogle Scholar
[14]Renyi, A.. Probability Theory. North Holland, (1970). (p. 391).Google Scholar
[15]Sullivan, D.. On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions. Annals of Math. Studies, 97 (1979), 465–496.Google Scholar
[16]Sullivan, D.. The density at infinity of a discrete group of hyperbolic motions. Publ. Math. IHES 50 (1980), 171–202.CrossRefGoogle Scholar
[17]Thurston, W.. Geometry and topology of 3-manifolds. Preprint, (1978).Google Scholar
[18]Tsuji, M.. Potential theory in modern function theory. Maruzen Co. Ltd: Tokyo, 1959.Google Scholar