1. CMB 2006 (vol 49 pp. 337)
|Homotopy Equivalence and Groups of Measure-Preserving Homeomorphisms |
It is shown that the group of compactly supported, measure-preserving homeomorphisms of a connected, second countable manifold is locally contractible in the direct limit topology. Furthermore, this group is weakly homotopically equivalent to the more general group of compactly supported homeomorphisms.
2. 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