论文标题
弱K.A.M.解决方案和最小化扭曲图的轨道
Weak K.A.M. solutions and minimizing orbits of twist maps
论文作者
论文摘要
对于环形的确切符号扭曲图，我们可以选择弱K.A.M.的选择。解决方案$ u_c = u（\ cdot，c）$，以lipschitz-collogy class $ c $的方式取决于lipschitz的方式。这使我们能够在弱K.A.M.之间建造桥梁。 Fathi理论，由Bangert开发的半孔的Aubry-Mather理论以及Katnelson \＆Ornstein所看到的落后不变的伪变性。我们推断出对弱K.A.M.的伪扫描的非常精确的描述。解决方案和许多有趣的结果 - Aubry妈妈集包含在其旋转数字垂直排序的伪扫描中； - 在环的垂直方向的每个图像中，最多有两个点，其负轨道通过给定的旋转数量最小化； - 所有相应的伪扫描都通过最小化的半孔填充，我们提供了较小的完整伪扫描选择的描述，其结合包含所有最小化的轨道； - 存在一个精确的符号扭曲图，其具有最小的负半轨道，而弱k.a.m.的伪扫描中不包含。解决方案。
For exact symplectic twist maps of the annulus, we etablish a choice of weak K.A.M. solutions $u_c=u(\cdot, c)$ that depend in a Lipschitz-continuous way on the cohomology class $c$. This allows us to make a bridge between weak K.A.M. theory of Fathi, Aubry-Mather theory for semi-orbits as developped by Bangert and existence of backward invariant pseudo-foliations as seen by Katnelson \& Ornstein. We deduce a very precise description of the pseudographs of the weak K.A.M. solutions and many interesting results as --the Aubry-Mather sets are contained in pseudographs that are vertically ordered by their rotation numbers; --on every image of a vertical of the annulus, there is at most two points whose negative orbit is minimizing with a given rotation number; --all the corresponding pseudographs are filled by minimizing semi-orbits and we provide a description of a smaller selection of full pseudographs whose union contains all the minimizing orbits; --there exists an exact symplectic twist map that has a minimizing negative semi-orbit that is not contained in the pseudograph of a weak K.A.M. solution.
