Minimal dynamical systems on the product of the Cantor set and the circle II

Abstract.

Let X be the Cantor set and φ be a minimal homeomorphism on $X \times \mathbb{T}$. We show that the crossed product C^*-algebra $C*(X \times \mathbb{T}, \varphi)$ is a simple A $\mathbb{T}$-algebra provided that the associated cocycle takes its values in rotations on $\mathbb{T}$. Given two minimal systems $(X \times \mathbb{T}, \varphi)$ and $(Y \times \mathbb{T}, \psi)$ such that φ and ψ arise from cocycles with values in isometric homeomorphisms on $\mathbb{T}$, we show that two systems are approximately K-conjugate when they have the same K-theoretical information.