Infinitely many periodic orbits in non-exact oscillating magnetic fields on surfaces with genus at least two for almost every low energy level

Abstract

In this paper we consider oscillating non-exact magnetic fields on surfaces with genus at least two and show that for almost every energy level $k$ below a certain value ${\tau }_{+}^{\ast }(g,\sigma )$ less than or equal to the "Mañé critical value of the universal cover" there are infinitely many closed magnetic geodesics with energy $k$.

In this version we corrected some minor inaccuracies and we improved the exposition following the precious suggestions of the anonymous referee. Accepted for publication in "Calculus of Variations and Partial Differential Equations". Comments are very welcome. arXiv admin note: text overlap with arXiv:1404.7641 by other authors

References in corpus (2)

• Infinitely many periodic orbits of exact magnetic flows on surfaces for almost every subcritical energy level
• On the Conley Conjecture for Reeb Flows

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• Periodic orbits in virtually contact structures
• On the rigidity of Zoll magnetic systems on surfaces
• Waist theorems for Tonelli systems in higher dimensions
• Lecture notes on closed orbits for twisted autonomous Tonelli Lagrangian flows