1. CMB 2002 (vol 45 pp. 97)
|Invariant Measures and Natural Extensions |
We study ergodic properties of a family of interval maps that are given as the fractional parts of certain real M\"obius 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:Continued fractions, interval maps, invariant measures
Categories:11J70, 58F11, 58F03