Polynomial integrals of magnetic geodesic flows on the 2-torus on\n several energy levels

2018/12/04 by С. И. Агапов, Agapov, Sergey, Alexandr Valyuzhenich +1
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1812.01290

Abstract

In this paper the geodesic flow on a 2-torus in a non-zero magnetic field is\nconsidered. Suppose that this flow admits an additional first integral F on\nN+2 different energy levels which is polynomial in momenta of arbitrary\ndegree N with analytic periodic coefficients. It is proved that in this case\nthe magnetic field and metrics are functions of one variable and there exists a\nlinear in momenta first integral on all energy levels.\n

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