 
Summary: On the existence of absolutely continuous conformal
measures for uniquely ergodic minimal Cantor
homeomorphisms
By KONSTANTIN ATHANASSOPOULOS
Department of Mathematics, University of Crete, GR71409 Iraklion, Greece
email: athanako@math.uoc.gr
Abstract
We prove an existence criterion for absolutely continuous conformal measures in the
case of uniquely ergodic minimal homeomorphisms of Cantor sets. It is applied to the
case of a Denjoy C1 diffeomorphism T of the circle in order to examine when log T is a
continuous coboundary on the unique Cantor minimal set of T.
1. Introduction
Let X be a compact metric space, T : X X a continuous transformation and
f : X R a continuous function. A Borel probability measure on X is called an
ef conformal measure for T if
X
d =
X
( T)ef
d
