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.
A non-squeezing theorem for convex symplectic images of the Hilbert ball
ABBONDANDOLO, ALBERTO;MAJER, PIETRO
2015-01-01
Abstract
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.File in questo prodotto:
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