Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
On the existence of absolutely continuous conformal measures for uniquely ergodic minimal Cantor
 

Summary: On the existence of absolutely continuous conformal
measures for uniquely ergodic minimal Cantor
homeomorphisms
By KONSTANTIN ATHANASSOPOULOS
Department of Mathematics, University of Crete, GR-71409 Iraklion, Greece
e-mail: 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

  

Source: Athanassopoulos, Konstantin - Department of Mathematics, University of Crete

 

Collections: Mathematics