Integrable magnetic flows on the two-torus: Zoll examples and systolic inequalities (1909.13821v1)

Published 30 Sep 2019 in math.DS and math.SG

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.

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