2015/12/16 by Martins, Gabriel
#70H07 (Secondary) #78A30 (Primary) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1512.05308
Inspired by a question of Colin de Verdière and Truc we study the dynamics of a classical charged particle moving in a bounded planar domain Ω under the influence of a magnetic field B which blows up at the boundary of the domain. We prove that under appropriate blow-up conditions the particle will never reach the boundary. As a corollary we obtain completeness of the magnetic flow. Our blow-up condition is that B should not be integrable along normal rays to the boundary, while its tangential derivative should be integrable along those same rays.