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Infinite-dimensional symplectic non-squeezing using non-standard analysis (1501.05905v5)
Published 23 Jan 2015 in math.SG, math-ph, math.LO, and math.MP
Abstract: We prove a non-squeezing result for infinite-dimensional Hamiltonian flows using non-standard model theory. For this we prove the existence of a corresponding family of pseudoholomorphic spheres and characterize the maximal time in terms of a limiting behaviour for these curves. While our proof is based on the finite-dimensional results from Gromov's original proof, we do not ask for any prior knowledge of non-standard model theory.