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

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

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