Integrable magnetic flows on the two-torus: Zoll examples and systolic inequalities
Dynamical Systems
2019-10-01 v1 Symplectic Geometry
Abstract
In this paper we study some aspects of integrable magnetic systems on the two-torus. On the one hand, we construct the first non-trivial examples with the property that all magnetic geodesics with unit speed are closed. On the other hand, we show that those integrable magnetic systems admitting a global surface of section satisfy a sharp systolic inequality.
Keywords
Cite
@article{arxiv.1909.13821,
title = {Integrable magnetic flows on the two-torus: Zoll examples and systolic inequalities},
author = {Luca Asselle and Gabriele Benedetti},
journal= {arXiv preprint arXiv:1909.13821},
year = {2019}
}
Comments
11 pages, 2 figures