Non-resonant circles for strong magnetic fields on surfaces

2021/04/14 by Asselle, L., Benedetti, G. · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2104.06733

Abstract

We study non-resonant circles for strong magnetic fields on a closed, connected, oriented surface and show how these can be used to prove the existence of trapping regions and of periodic magnetic geodesics with prescribed low speed. As a corollary, there exist infinitely many periodic magnetic geodesics for every low speed in the following cases: i) the surface is not the two-sphere, ii) the magnetic field vanishes somewhere.

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• The growth rate of closed prime magnetic geodesics on closed contact manifolds

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