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Abstract We study ergodic properties of a family of intervalmaps 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.
Andrew Haas (Fri,) studied this question.