论文标题
在维度2中通过曲线对曲线叶子的符号同构/差异性的作用
Actions of symplectic homeomorphisms/diffeomorphisms on foliations by curves in dimension 2
论文作者
论文摘要
本文的两个主要结果涉及二维环形的C0可融合符合性扭转差异的规律性，即$ \ bullet $ bulter $这种叶子的生成函数是C1； $ \ bullet $ foliation是h {Ö} lder，带有指数1/2。我们还通过图形的图表来表征，这些图形可以通过符号同构形态形态矫正，并证明每种符号的同构同构使不变的所有叶子不变的叶子的所有叶子都具有arnol'd-liouville坐标，在这种坐标中，动力学限制在叶子上限制为旋转。我们推断，二维环的每个Lipschitz都具有arnol'd-liouville的坐标，然后在平滑曲线中提供“奇怪”的lipschitions的例子，这些曲线无法通过一种符号的同音态度来抗衡，并在平滑的曲线中提供“奇怪” lipschitz叶子的示例作者，题为弱K.A.M.的横向依赖性。在重写H {Ö} lder部分的蚂蚁添加后，用于符号扭转图的解决方案。
The two main results of this paper concern the regularity of the invariant foliation of a C0-integrable symplectic twist diffeomorphisms of the 2-dimensional annulus, namely that $\bullet$ the generating function of such a foliation is C1 ; $\bullet$ the foliation is H{ö}lder with exponent 1/2. We also characterize foliations by graphs that are straightenable via a symplectic homeomorphism and prove that every symplectic homeomorphism that leaves invariant all the leaves of a straightenable foliation has Arnol'd-Liouville coordinates, in which the Dynamics restricted to the leaves is conjugated to a rotation. We deduce that every Lipschitz integrable symplectic twist diffeomorphisms of the 2-dimensional annulus has Arnol'd-Liouville coordinates and then provide examples of 'strange' Lipschitz foliations in smooth curves that cannot be straightened by a symplectic homeomorphism and cannot be invariant by a symplectic twist diffeomorphism.This article is a part of another preprint of the authors, entitled On the transversal dependence of weak K.A.M. solutions for symplectic twist maps, after rewriting ant adding of the H{ö}lder part.
