A non-squeezing theorem for convex symplectic images of the Hilbert ball (Q745554)

The aim of this work is to extend the non-squeezing theorem of Gromov to symplectomorphisms of an infinite-dimensional Hilbert space, under the assumption that the image of the ball is convex. A main tool is a symplectomorphism which maps a bounded closed convex neighborhood of the origin into its interior part. This map is constructed from a convex coercive Hamiltonian which does not admit non-constant periodic orbits. The proof of the main result is contained in Sections 5--9.