On totally integrable magnetic billiards on constant curvature surface

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Abstract

We consider billiard ball motion in a convex domain of a constant curvature surface influenced by the constant magnetic field. We prove that if the billiard map is totally integrable then the boundary curve is necessarily a circle. This result shows that the so-called Hopf rigidity phenomenon which was recently obtained for classical billiards on constant curvature surfaces holds true also in the presence of constant magnetic field.

Original languageEnglish
Pages (from-to)112-119
Number of pages8
JournalElectronic Research Announcements in Mathematical Sciences
Volume19
DOIs
StatePublished - 2012

Keywords

  • Hopf rigidity
  • Magnetic Billiards
  • Mirror formula

All Science Journal Classification (ASJC) codes

  • General Mathematics

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