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arXiv · 1411.3989

Symplectic non-squeezing in Hilbert space and discrete Schr\"odinger equations

Alexandre Sukhov·Alexander Tumanov
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Abstract

We prove a generalization of Gromov's symplectic non-squeezing theorem for the case of Hilbert spaces. Our approach is based on filling almost complex Hilbert spaces by complex discs partially extending Gromov's results on existence of $J$-complex curves. We apply our result to the flow of the discrete nonlinear Schr\"odinger equation.

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Alexandre Sukhov, Alexander Tumanov. 2014-11-14. Symplectic non-squeezing in Hilbert space and discrete Schr\"odinger equations. https://arxiv.org/abs/1411.3989

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