English

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