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.
Integrable Magnetic Flows on the Two-Torus: Zoll Examples and Systolic Inequalities / Asselle, L.; Benedetti, G.. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 31:3(2021), pp. 2924-2940. [10.1007/s12220-020-00379-1]
Integrable Magnetic Flows on the Two-Torus: Zoll Examples and Systolic Inequalities
Asselle L.;Benedetti G.
2021-01-01
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.File in questo prodotto:
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