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

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.

arXiv comment27 pages, 6 figures

Cited by in corpus (5)

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• Counting Periodic Trajectories of Finsler Billiards
• Finsler metrics on surfaces admitting three projective vector fields
• Algebraic non-integrability of magnetic billiards