Non-homogeneous extensions of Cantor minimal systems

Extensions of Cantor Minimal Systems and Dimension Groups

Given a factor map p : (X, T )→ (Y, S) of Cantor minimal systems, we study the relations between the dimension groups of the two systems. First, we interpret the torsion subgroup of the quotient of the dimension groups K0(X)/K0(Y ) in terms of intermediate extensions which are extensions of (Y, S) by a compact abelian group. Then we show that, by contrast, the existence of an intermediate non-a...

Real Coboundaries for Minimal Cantor Systems

In this paper we investigate the role of real-valued coboundaries for classifying of minimal homeomorphisms of the Cantor set. This work follows the work of Giordano, Putnam, and Skau who showed that one can use integer-valued coboundaries to characterize minimal homeomorphisms up to strong orbit equivalence. First, we prove a rigidity result. We show that there is an orbit equivalence between ...

Flow-orbit Equivalence for Minimal Cantor Systems

This paper is about ‡ow-orbit equivalence, a topological analogue of even Kakutani equivalence. In addition to establishing many basic facts about this relation, we characterize the conjugacies of induced systems that can be extended to a ‡ow-orbit equivalence. We also describe the relationship between ‡ow-orbit equivalence and a distortion function of an orbit equivalence. We show that if the ...

Minimal Cantor Systems and Unimodal Maps

Dimension of the harmonic measure of non-homogeneous Cantor sets

We prove that the dimension of the harmonic measure of the complementary of a translation-invariant type of Cantor sets as a continuous function of the parameters determining these sets. This results extend a previous one of the author and do not use ergodic theoretic tools, not applicable to our case.