We prove that the non-squeezing theorem of Gromov holds for symplectomor- phisms on an infinite-dimensional symplectic Hilbert space, under the assumption that the image of the ball is convex. The proof is based on the construction by dual- ity methods of a symplectic capacity for bounded convex neighbourhoods of the ori- gin. We also discuss some examples of symplectomorphisms on infinite-dimensional spaces exhibiting behaviours which would be impossible in finite dimensions.
|Autori interni:||ABBONDANDOLO, ALBERTO|
|Autori:||Abbondandolo A.; Majer P.|
|Titolo:||A non-squeezing theorem for convex symplectic images of the Hilbert ball|
|Anno del prodotto:||2015|
|Appare nelle tipologie:||1.1 Articolo in rivista|