Gromov's non-squeezing theorem and its applications to Hamiltonian flows
ABSTRACT :
It is well-known that the Hamiltonian flows are volume preserving. In these lectures we will review how the Hamiltonian flow preserves the canonical symplectic form on the co-tangent bundle. We will use this fact together with the so called psuedo- holomorphic curves to establish new constraints on the behavior of Hamiltonian flows.Lectures are aimed at people with physics background. Any student with a sound knowledge of the first course on classical mechanics can understand these lectures.