论文标题
分析伪旋转
Analytic pseudo-rotations
论文作者
论文摘要
我们构建了圆柱体或球体的分析符号切除术，具有零或两个周期性点，并且不连接到旋转。在圆柱体的情况下，我们表明可以选择这些符号切除型，也可以与最大秩序的局部出现相反。特别是，这反驳了Birkhoff（1941）的猜想，并解决了Herman（1998）的问题。证明的一个方面提供了一个新的近似定理，它尤其可以在新的分析设置中实现Anosov-Katok方案。
We construct analytic symplectomorphisms of the cylinder or the sphere with zero or exactly two periodic points and which are not conjugated to a rotation. In the case of the cylinder, we show that these symplectomorphisms can be chosen ergodic or to the contrary with local emergence of maximal order. In particular, this disproves a conjecture of Birkhoff (1941) and solve a problem of Herman (1998). One aspect of the proof provides a new approximation theorem, it enables in particular to implement the Anosov-Katok scheme in new analytic settings.
