辛拓扑中一些问题的研究

Hofer几何是辛拓扑中的重要分在支，我们将研究Hamiltonian微分同胚群Ham (M, ω) 中关于Hofer度量的极小测地线猜测及这个群的直径的无穷大猜测，还将探讨辛拓扑中的流坎虏狻einstein 猜测及退化的Arnold 猜测。这些问题都为辛拓扑中的基本问题。它们睦斫庥虢饩龆杂谛镣仄说睦斫狻⑹У耐骋恍浴⑽锢砑傲ρУ纳羁倘鲜抖季哂猩钤兜囊庖濉

Supported by the national natural science foundation of China we have studied the.following symplectic topology questions. We defined the Gromov-Witten invariants.on noncompact semipositive geometrically bounded symplectic manifolds and used.them to study the rigidity of Hamiltonian loops with compact support on this kind of manifolds. We also established pseudo symplectic capacity theory and related it.Gromov-Witten invariants; As applications we got a very general nonsqueezing.theorem， proved Weinstein conjecture for more large class of symplectic manifolds.and extended Biran’s Lagrangian barrier theorem to arbitrary closed symplectic.manifolds. We constructed an explicit isomorphism between Floer homology and.quantum homology on any closed symplectic manifolds. In addition we also studied.the periodic motion of a charge in a magnetic fields, and in a joint work with.Professor Long yiming we proved that the autonomous Lagrange system possess.infinitely many geometrically different periodic orbits.