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

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