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arXiv · 1405.3200

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

Alberto Abbondandolo·Pietro Majer
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Abstract

We prove that the non-squeezing theorem of Gromov holds for symplectomorphisms 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 duality methods of a symplectic capacity for bounded convex neighbourhoods of the origin. We also discuss some examples of symplectomorphisms on infinite-dimensional spaces exhibiting behaviours which would be impossible in finite dimensions.

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Alberto Abbondandolo, Pietro Majer. 2014-05-13. A non-squeezing theorem for convex symplectic images of the Hilbert ball. https://arxiv.org/abs/1405.3200

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