论文标题
$ c^1 $ c^2 $ circle diffemormormormists与刚性旋转的不理性和规律性之间的关系
Relation between irrationality and regularity for $ C^1 $ conjugacy of $ C^2 $ circle diffeomorphisms to rigid rotations
论文作者
论文摘要
通过引入连续性模量，我们首先在$ C^2 $平滑度下建立相应的交叉比例失真估计，并进一步给出Denjoy型不平等，这几乎是处理圆形差异性的最佳选择。后者在$ c^1 $与非理性旋转的结合中起着重要作用。我们还首次给出了连续性和非理性之间的明确集成性相关性。此外，还考虑了结合的规律性，并被证明是锋利的。
By introducing the modulus of continuity, we first establish the corresponding cross-ratio distortion estimates under $ C^2 $ smoothness, and further give a Denjoy-type inequality, which is almost optimal in dealing with circle diffeomorphisms. The latter plays a prominent role in the study of $ C^1 $ conjugacy to irrational rotations. We also give the explicit integrability correlation between continuity and irrationality for the first time. Further the regularity of the conjugation is also considered and proved to be sharp.
