Billiards in Finsler and Minkowski geometries

Eugene Gutkin, Serge Tabachnikov

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

We begin the study of billiard dynamics in Finsler geometry. We deduce the Finsler billiard reflection law from the “least action principle”, and extend the basic properties of Riemannian and Euclidean billiards to the Finsler and Minkowski settings, respectively. We prove that the Finsler billiard map is a symplectomorphism, and compute the mean free path of the Finsler billiard ball. For the planar Minkowski billiard we obtain the mirror equation, and extend the Mather's non-existence of caustics result. We establish an orbit-to-orbit duality for Minkowski billiards.

Original languageEnglish (US)
Pages (from-to)277-301
Number of pages25
JournalJournal of Geometry and Physics
Volume40
Issue number3-4
DOIs
StatePublished - Jan 1 2002

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Billiards
orbits
geometry
mean free path
balls
alkalies
mirrors
Orbit
Finsler Geometry
Caustic
Nonexistence
Deduce
Euclidean
Mirror
Duality
Ball
Path

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Geometry and Topology

Cite this

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Billiards in Finsler and Minkowski geometries. / Gutkin, Eugene; Tabachnikov, Serge.

In: Journal of Geometry and Physics, Vol. 40, No. 3-4, 01.01.2002, p. 277-301.

Research output: Contribution to journalArticle

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