Infinite-dimensional symplectic non-squeezing using non-standard analysis
arXiv:1501.05905
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.
38 pages. Based on the feedback of an anonymous referee we have strengthened our existence result for pseudoholomorphic spheres; in particular, we now give a characterization of the maximal time in terms of a limiting behaviour for these curves