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.

中文翻译：

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关于 Zoll 磁系统在表面上的刚度

在本文中，我们研究了 Zoll 磁系统在封闭表面上的刚性方面。我们将由恒定曲率度量和恒定磁函数给出的正属表面上的磁系统表征为唯一的磁系统，使得相关的哈密顿流是 Zoll，即每个轨道都是封闭的，在每个能级。我们还证明了在不同情况下磁扰动下可能退化的闭合测地线的持久性。