Infinite-dimensional symplectic non-squeezing using non-standard analysis
Symplectic Geometry
2018-06-19 v5 Mathematical Physics
Logic
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.
Keywords
Cite
@article{arxiv.1501.05905,
title = {Infinite-dimensional symplectic non-squeezing using non-standard analysis},
author = {Oliver Fabert},
journal= {arXiv preprint arXiv:1501.05905},
year = {2018}
}
Comments
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