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

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dc.creatorTabachnikov, Serge
dc.date2003-02-24
dc.date.accessioned2026-07-07T04:55:31Z
dc.date.available2026-07-07T04:55:31Z
dc.descriptionWe 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.
dc.description27 pages, 6 figures
dc.identifierhttps://arxiv.org/abs/math/0302288
dc.identifierhttp://arxiv.org/abs/math/0302288
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/66607
dc.subjectDifferential Geometry
dc.subjectDynamical Systems
dc.subject53B40, 53C60, 53C65, 70F35
dc.titleRemarks on magnetic flows and magnetic billiards, Finsler metrics and a magnetic analog of Hilbert's fourth problem
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