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arXiv · 1510.00152

On the periodic motions of a charged particle in an oscillating magnetic field on the two-torus

Luca Asselle·Gabriele Benedetti
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Abstract

Let $(\mathbb T^2,g)$ be a Riemannian two-torus and let $σ$ be an oscillating $2$-form on $\mathbb T^2$. We show that for almost every small positive number $k$ the magnetic flow of the pair $(g,σ)$ has infinitely many periodic orbits with energy $k$. This result complements the analogous statement for closed surfaces of genus at least $2$ [Asselle and Benedetti, Calc. Var. Partial Differential Equations, 2015] and at the same time extends the main theorem in [Abbondandolo, Macarini, Mazzucchelli, and Paternain, J. Eur. Math. Soc. (JEMS), to appear] to the non-exact oscillating case.

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Luca Asselle, Gabriele Benedetti. 2016-09-15. On the periodic motions of a charged particle in an oscillating magnetic field on the two-torus. https://doi.org/10.1007/s00209-016-1787-6

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