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arXiv · 1910.03285

On the rigidity of Zoll magnetic systems on surfaces

Luca Asselle·Christian Lange
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Abstract

In this paper we study rigidity aspects of Zoll magnetic systems on closed surfaces. We characterize magnetic systems on surfaces of positive genus given by constant curvature metrics and constant magnetic functions as the only magnetic systems such that the associated Hamiltonian flow is Zoll, i.e. every orbit is closed, on every energy level. We also prove the persistence of possibly degenerate closed geodesics under magnetic perturbations in different instances.

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Luca Asselle, Christian Lange. 2019-10-08. On the rigidity of Zoll magnetic systems on surfaces. https://doi.org/10.1088/1361-6544%2Fab839c

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