Abstract
AbstractIn 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.
Publisher
Springer Science and Business Media LLC
Reference15 articles.
1. Abbondandolo, A., Bramham, B., Hryniewicz, U.L., Salomão, P.A.S.: A systolic inequality for geodesic flows on the two-sphere. Math. Ann. 367(1–2), 701–753 (2017)
2. Abbondandolo, A., Bramham, B., Hryniewicz, U.L., Salomão, P.A.S.: Sharp systolic inequalities for Reeb flows on the three-sphere. Invent. Math. 211(2), 687–778 (2018)
3. Abbondandolo, A., Bramham, B., Hryniewicz, U.L., Salomão, P.A.S.: Sharp systolic inequalities for Riemannian and Finsler spheres of revolution, arXiv:1808.06995, preprint (2018)
4. Asselle, L., Benedetti, G.: The Lusternik–Fet theorem for autonomous Tonelli Hamiltonian systems on twisted cotangent bundles. J. Topol. Anal. 8(3), 545–570 (2016)
5. Asselle L., Lange, C.: On the rigidity of Zoll magnetic systems on surfaces, arXiv:1910.03285, preprint (2019)
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