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.  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.

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