Coisotropic Submanifolds of Symplectic Manifolds and Leafwise Fixed Points
主 题: Coisotropic Submanifolds of Symplectic Manifolds and Leafwise Fixed Points
报告人: Fabian Ziltener
时 间: 2017-02-23 14:00 - 2017-02-23 15:00
地 点: Room 77201，Jingchunyuan 78,BICMR
\n\tConsider a symplectic manifold\n$(M,\\omega)$, a closed coisotropic submanifold $N$ of $M$, and a Hamiltonian\ndiffeomorphism $\\phi$ on $M$. A leafwise fixed point for $\\phi$ is a point\n$x\\in N$ that under $\\phi$ is mapped to its isotropic leaf. These points generalize\nfixed points and Lagrangian intersection points. In classical mechanics\nleafwise fixed points correspond to trajectories that are changed only by a\ntime-shift, when an autonomous mechanical system is perturbed in a\ntime-dependent way.
\n\tJ. Moser posed the following problem: Find conditions under which\nleafwise fixed points exist and provide a lower bound on their number. A\nspecial case of this problem is V.I. Arnold\'s conjecture about fixed points of\nHamiltonian diffeomorphisms.
\n\tIn this talk the speaker will\nprovide solutions to Moser\'s problem. As an application, the sphere is not\nsymplectically squeezable. This improves M. Gromov\'s symplectic nonsqueezing\nresult.