论文标题
Denjoy子系统和马蹄铁
Denjoy sub-systems and horseshoes
论文作者
论文摘要
我们引入了一个弱的Denjoy子系统（WDS）的概念，该概念将Aubry-Mather Cantor设置概括为歧管的差异性。我们解释了如何与这样的WD相关联。然后，我们在任何马蹄形中建造一个连续的一个参数家族，其旋转编号索引。在Aubry-Ather理论的环境中，查看反问题，我们还证明，对于环形的通用保守性扭曲图，大多数Aubry-Mather集合都包含在某些马蹄形中，该曲线与具有合理旋转数的Aubry-Mather组相关。
We introduce a notion of weak Denjoy subsystem (WDS) that generalizes the Aubry-Mather Cantor sets to diffeomorphisms of manifolds. We explain how a rotation number can be associated to such a WDS. Then we build in any horseshoe a continuous one parameter family of such WDS that is indexed by its rotation number. Looking at the inverse problem in the setting of Aubry-Mather theory, we also prove that for a generic conservative twist map of the annulus, the majority of the Aubry-Mather sets are contained in some horseshoe that is associated to a Aubry-Mather set with a rational rotation number.
