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.
2015
Abbondandolo, Alberto; Majer, Pietro
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/500067
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 22
  • ???jsp.display-item.citation.isi??? 19
social impact