Let \(M\) be a closed manifold and \(L\) an exact magnetic Lagrangian. In this paper we prove that there exists a residual set \(\mathcal{G}\) of \(H^{1}\left(M;\mathbb{R}\right)\) such that the property

with \({\widetilde{\mathcal{M}}}\left(c\right)\) supporting a uniquely ergodic measure, is generic in the family of exact magnetic Lagrangians. We also prove that, for a fixed cohomology class \(c\), there exists a residual set of exact magnetic Lagrangians such that, when this unique measure is supported on a periodic orbit, this orbit is hyperbolic and its stable and unstable manifolds intersect transversally. This result is a version of an analogous theorem, for Tonelli Lagrangians, proven in [6].

令\(M\)是一个封闭的流形，而\(L\)是一个精确的磁性拉格朗日。在本文中，我们证明了存在的残留组\（\ mathcal {G} \）的\（H ^ {1} \左（M; \ mathbb {R} \右）\） ，使得所述属性

与\（{\ widetilde {\ mathcal {M}}} \左（C \右）\）支撑一个独特遍历测量，是在家庭中的确切磁拉氏的通用的。我们还证明，对于固定的上同调类\(c\)，存在一组精确的磁拉格朗日量，使得当这个独特的测度被支持在一个周期轨道上时，这个轨道是双曲线的，并且它的稳定和不稳定的流形相交横向。对于 Tonelli Lagrangians，该结果是类似定理的一个版本，在 [6] 中得到证明。