2020/03/20 by Luca Asselle, Asselle, Luca, Gabriele Benedetti +1
Mathematics · Physics and Astronomy · #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2003.09141
We prove a normal form for strong magnetic fields on a closed, oriented\nsurface and use it to derive two dynamical results for the associated flow.\nFirst, we show the existence of KAM tori and trapping regions provided a\nnatural non-resonance condition holds. Second, we prove that the flow cannot be\nZoll unless (i) the Riemannian metric has constant curvature and the magnetic\nfunction is constant, or (ii) the magnetic function vanishes and the metric is\nZoll. We complement the second result by exhibiting an exotic magnetic field on\na flat two-torus yielding a Zoll flow for arbitrarily small rescalings.\n