Floer theory for Hamiltonian PDE using model theory
Abstract
Under natural restrictions it is known that a nonlinear Schr\"odinger equation is a Hamiltonian PDE which defines a symplectic flow on a symplectic Hilbert space preserving the Hilbert norm. When the potential is one-periodic in time and after passing to the projectivization, it makes sense to ask whether the natural analogue of the Arnold conjecture holds. By employing methods from non-standard model theory we show how Hamiltonian Floer theory can be generalized from finite to infinite dimensions. While our proof entirely builds on finite-dimensional results, we do not ask for any prior knowledge of non-standard model theory.
Keywords
Cite
@article{arxiv.1507.00482,
title = {Floer theory for Hamiltonian PDE using model theory},
author = {Oliver Fabert},
journal= {arXiv preprint arXiv:1507.00482},
year = {2018}
}
Comments
48 pages; more details, explanations, and an unnecessary redundancy removed: by proving near-standardness after proving limitedness of derivatives, an extra a priori estimate is no longer needed