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

2014/11/14 by Alexandre Sukhov, Sukhov, Alexandre, Alexander Tumanov +1
Mathematics · #32H02 #53C15 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1411.3989

openalex publication_date 2014/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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