Two minimal unique ergodic diffeomorphisms on a manifolds and their smooth crossed product algebras

Abstract

In this article we construct two minimal unique ergodic diffeomorphisms $\alpha$ and $\beta$ on $S^3\times S^6\times S^8$. We will show that $C(S^3\times S^6\times S^8){⋊}_{\alpha }\mathbb{Z}$ and $C(S^3\times S^6\times S^8){⋊}_{\beta }\mathbb{Z}$ are equivalent to each other, while $C^{\infty }(S^3\times S^6\times S^8){⋊}_{\alpha }\mathbb{Z}$ and $C^{\infty }(S^3\times S^6\times S^8){⋊}_{\beta }\mathbb{Z}$ are not.