论文标题
没有完全的数值不变，可以使圆形差异的平滑缀合性
There is no complete numerical invariant for smooth conjugacy of circle diffeomorphisms
论文作者
论文摘要
Poincaré和Denjoy的经典结果表明，当且仅当它们具有相同的旋转号时，圆圈的两个方向$ C^2 $差异性在拓扑上是共轭的。我们表明，没有可能通过具有较高规律性的同构形态学来获得这种完全的数值鲍尔不变性。例如，我们考虑Hölder同构的共轭或$ c^k $ -diffeomorphisms与$ k \ in \ Mathbb {z}^+ cup \ cup \ {\ infty \} $。该证明结合了描述性集理论的技术和通过共轭方法的近似方法的定量版本，用于圆形差异。
Classical results by Poincaré and Denjoy show that two orientation-preserving $C^2$ diffeomorphisms of the circle are topologically conjugate if and only if they have the same rotation number. We show that there is no possibility of getting such a complete numerical Borel invariant for the conjugacy relation of orientation-preserving circle diffeomorphisms by homeomorphisms with higher degree of regularity. For instance, we consider conjugacy by Hölder homeomorphisms or by $C^k$-diffeomorphisms with $k\in \mathbb{Z}^+ \cup \{\infty\}$. The proof combines techniques from Descriptive Set Theory and a quantitative version of the Approximation by Conjugation method for circle diffeomorphisms.
