Geodesic
Invariant Measures and Natural Extensions
Canadian mathematical bulletin, Tome 45 (2002) no. 1, pp. 97-108

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DOI

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.
DOI : 10.4153/CMB-2002-011-4
Mots-clés : 11J70, 58F11, 58F03, Continued fractions, interval maps, invariant measures 
Haas, Andrew. Invariant Measures and Natural Extensions. Canadian mathematical bulletin, Tome 45 (2002) no. 1, pp. 97-108. doi: 10.4153/CMB-2002-011-4
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     title = {Invariant {Measures} and {Natural} {Extensions}},
     journal = {Canadian mathematical bulletin},
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     year = {2002},
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     number = {1},
     doi = {10.4153/CMB-2002-011-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2002-011-4/}
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