Algebraic Birkhoff conjecture for billiards on Sphere and Hyperbolic plane

  • Misha Bialy*
  • , Andrey E. Mironov
  • *Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

We consider a convex curve γ lying on the Sphere or Hyperbolic plane. We study the problem of existence of polynomial in velocities integrals for Birkhoff billiard inside the domain bounded by γ. We extend the result by S. Bolotin (1992) and get new obstructions on polynomial integrability in terms of the dual curve Γ. We follow a method which was introduced by S. Tabachnikov for Outer billiards in the plane and was applied later on in our recent paper to Birkhoff billiards with the help of a new the so called Angular billiard.

Original languageEnglish
Pages (from-to)150-156
Number of pages7
JournalJournal of Geometry and Physics
Volume115
DOIs
StatePublished - 1 May 2017

Funding

FundersFunder number
Russell Sage Foundation14-11-00441
Israel Science Foundation162/15

    Keywords

    • Birkhoff billiards
    • Outer billiards
    • Polynomial integrals

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