Remarks on magnetic flows and magnetic billiards, Finsler metrics and a magnetic analog of Hilbert's fourth problem

2003/02/24 by Serge Tabachnikov, Tabachnikov, Serge
Mathematics · #53B40 #53C60 #53C65 #70F35 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #math.DG #math.DS #msc:53B40 #msc:53C60 #msc:53C65 #msc:70F35

paper · pdf · doi:10.48550/arxiv.math/0302288

27 pages, 6 figures

arxiv created 2003/02/24 · arxiv updated 2009/11/30

Abstract

We interpret magnetic billiards as Finsler ones and describe an analog of the string construction for magnetic billiards. Finsler billiards for which the law "angle of incidence equals angle of reflection" are described. We characterize the Finsler metrics in the plane whose geodesics are circles of a fixed radius. This is a magnetic analog of Hilbert's fourth problem asking to describe the Finsler metrics whose geodesics are straight lines.

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