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Geometrical Markov coding of geodesics on surfaces of constant negative curvature

Published online by Cambridge University Press:  19 September 2008

Caroline Series
Caroline Series
Affiliation:
Mathematics Institute, University of Warwick, Coventry, CV4 7AL, England Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104, USA
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Abstract

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A natural geometrical representation of the geodesic flow on a surface M of constant negative curvature is given in which the base transformation is the shift on a (finite type) space of shortest words relative to a fixed generating set for π1(M) and the height function is the hyperbolic distance across a fundamental region for π1(M). This representation is obtained by comparing cutting sequences on M with generalised continued fraction expansions of endpoints on ℝ

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 6 , Issue 4 , December 1986 , pp. 601 - 625
Copyright
Copyright © Cambridge University Press 1986

References

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