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Invariant Measures and Natural Extensions

Published online by Cambridge University Press:  20 November 2018

Andrew Haas
Andrew Haas*
Affiliation:
Department of Mathematics, The University of Connecticut, Storrs, Connecticut 06269-3009, U.S.A., email: [email protected]
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Abstract

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We study ergodic properties of a family of interval maps that are given as the fractional parts of certain real Möbius transformations. Included are the maps that are exactly $n$-to-1, the classical Gauss map and the Renyi or backward continued fraction map. A new approach is presented for deriving explicit realizations of natural automorphic extensions and their invariant measures.

Keywords

11J7058F1158F03Continued fractionsinterval mapsinvariant measures
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 45 , Issue 1 , 01 March 2002 , pp. 97 - 108
Copyright
Copyright © Canadian Mathematical Society 2002

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