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}) \rtimes_\alpha \mathbb{Z} $ and $C(S^3 \times S^{6} \times S^{8})\rtimes_\beta \mathbb{Z} $ are equivalent to each other, while $C^\infty (S^3 \times S^{6} \times S^{8})\rtimes_\alpha \mathbb{Z} $ and $C^\infty(S^3 \times S^{6} \times S^{8} )\rtimes_\beta \mathbb{Z} $ are not.