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Backward continued fractions, Hecke groups and invariant measures for transformations of the interval

Published online by Cambridge University Press:  14 October 2010

Karlheinz Gröchenig  and
Andrew Haas
Karlheinz Gröchenig
Affiliation:
Department of Mathematics U-9, The University of Connecticut, Storrs, CT 06269-3009, USA, (e-mail: [email protected], [email protected])
Andrew Haas
Affiliation:
Department of Mathematics U-9, The University of Connecticut, Storrs, CT 06269-3009, USA, (e-mail: [email protected], [email protected])
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Abstract

We develop a new type of backward continued fractions that can be associated to each Hecke-type group. We study its symbolic dynamics, and the corresponding interval maps and their invariant measures. These measures are infinite if and only if the corresponding groups are discrete. For the discrete Hecke groups the invariant measure is computed explicitly by studying the geodesic flow on the associated Riemann surface.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 6 , December 1996 , pp. 1241 - 1274
Copyright
Copyright © Cambridge University Press 1996

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