C^0 integrability for twist map
报告题目(Title)：C^0 integrability for twist map
报告人(Speaker)：Marie-Claude Arnaud（IMJ-PRG, Université Paris-Diderot）
地点(Place)：Zoom: 62099877902 密码：123456
时间(Time)：11月2日 15：30-16：30
邀请人(Inviter)：苏喜锋
报告摘要
This is a joint work with Maxime Zavidovique. For Hamiltonian systems, the well-known Arnol’d-Liouville theorem tells us that if the system has enough C2 independent integrals, then the space is foliated by invariant Lagrangian submanifolds on which the Dynamics is conjugated to a rotation. We will consider a situation with weaker hypothesis: assume that a symplectic twist map of the annulus has an invariant foliation into continuous curve. What can be said on the this foliation and the Dynamics? After explaining some classical and less classical results in the Hamiltonian case, we will explain recent results on twist maps, e.g. that the invariant foliation is Holder, that with some other hypothesis the restricted dynamics to invariant curve is conjugate to a rotation.
主讲人简介
Marie-Claude Arnaud教授是2010年国际数学家大会（ICM）45分钟邀请报告人，在Green bundles, Aubry-Mather理论、弱KAM理论等领域非常活跃，其相关重要结果在《Annals of Mathematics》、《Publications Mathématiques Institut de Hautes Études Scientifiques》等国际顶尖期刊上发表。
