Different diffeomorphisms can give the same [Formula: see text] crossed product algebra. Our main purpose is to show that we can still classify dynamical systems with some appropriate smooth crossed product algebras when their corresponding [Formula: see text] crossed product algebras are isomorphic. For this purpose, we construct two minimal unique ergodic diffeomorphisms [Formula: see text] and [Formula: see text] of [Formula: see text]. The [Formula: see text] algebras classification theory, smooth crossed product algebras considered by R. Nest and cyclic cohomology are used to show that [Formula: see text] and [Formula: see text] give the same [Formula: see text] algebra and induce different smooth crossed product algebras.

中文翻译：

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流形和循环上同调的最小唯一遍历微分同胚的平滑叉积

不同的微分同胚可以给出相同的[公式：见正文]叉积代数。我们的主要目的是表明当动力系统对应的[公式：见正文]叉积代数是同构的时，我们仍然可以用一些适当的光滑叉积代数对动力系统进行分类。为此，我们构造了两个最小唯一遍历微分同胚[公式：见文本]和[公式：见文本]的[公式：见文本]。[公式：见文]代数分类理论、R.Nest考虑的平滑叉积代数和循环上同调用于证明[公式：见文]和[公式：见文]给出相同的[公式：见文]代数和诱导不同的光滑叉积代数。