Let $(\mathbb T^2,g)$ be a Riemannian two-torus and let $\sigma$ be anoscillating $2$-form on $\mathbb T^2$. We show that for almost every smallpositive number $k$ the magnetic flow of the pair $(g,\sigma)$ has infinitelymany periodic orbits with energy $k$. This result complements the analogousstatement for closed surfaces of genus at least $2$ [Asselle and Benedetti,Calc. Var. Partial Differential Equations, 2015] and at the same time extendsthe 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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机译：假设$（\ mathbb T ^ 2，g）$是黎曼二重奏，并且让$ \ sigma $使$ \ mathbb T ^ 2 $上的2 $-形式振荡。我们表明，几乎对于每个小的正数$ k $，对$（g，\ sigma）$的磁流都具有无限多个具有能量$ k $的周期性轨道。该结果补充了至少2美元的闭合类属的相似陈述[Asselle和Benedetti，Calc。变体偏微分方程，2015]，同时扩展了[Abbondandolo，Macarini，Mazzucchelli，和Paternain，J.Eur。数学。 Soc。 （JEMS），出现在非精确振荡的情况下。
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