Fundamental group of uniquely ergodic Cantor minimal systems

Topological Mixing and Uniquely Ergodic Systems

Every ergodic transformation (X, 7, :~,/z) has an isomorphic system (Y, U, ~, v) which is uniquely ergodic and topologically mixing.

Uniquely Ergodic Minimal Tiling Spaces with Positive Entropy

Strictly ergodic spaces of tilings with positive entropy are constructed using tools from information and probability theory. Statistical estimates are made to create a one-dimensional subshift with these dynamical properties, yielding a space of repetitive tilings of R with finite local complexity that is also equivalent to a symbolic dynamical system with a Z action.

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 ...

Existence of Non-uniform Cocycles on Uniquely Ergodic Systems

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 ...