Abstract
Let $X$ be an infinite compact metric space with finite covering dimension. Let $\af,\bt: X\to X$ be two minimal homeomorphisms. Suppose that the range of $K_0$-groups of both crossed products are dense in the space of real affine continuous functions on the tracial state space. We show that $\af$ and $\bt$ are approximately conjugate uniformly in measure if and only if they have affine homeomorphic invariant probability measure spaces.
Citation
Huaxin Lin. "Minimal homeomorphisms and approximate conjugacy in measure." Illinois J. Math. 51 (4) 1159 - 1188, Winter 2007. https://doi.org/10.1215/ijm/1258138537
Information