论文标题
关于扭曲地图和哈密顿流的可整合变形的刚性
On the rigidity of integrable deformations of twist maps and Hamiltonian flows
论文作者
论文摘要
在本文中，我们研究了圆柱体的可整合面积的扭曲图的刚性特性。更具体地说，我们证明，如果标准集成图的变形可保留旋转不变的圆圈（即，圆柱体的非平凡不变曲线，该曲线的动力学与旋转相结合），以使任何有理旋转的距离在开放的间隔中进行任何有理旋转的数量（无需对其大小上的任何假设），则必须进行缺陷。讨论了在更高维度中可集成的Tonelli Hamiltonian流动的模拟现象。
In this article we investigate rigidity properties of integrable area-preserving twist maps of the cylinder. More specifically, we prove that if a deformation of the standard integrable map preserves rotational invariant circles (i.e., homotopically non-trivial invariant curves of the cylinder on which the dynamics is conjugate to a rotation) for any rational rotation number in an open interval (without any further assumption on its size), then the deformation must be trivial. Analogue phenomena for integrable Tonelli Hamiltonian flows in higher dimensions are discussed.
