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Moscow University Mathematics Bulletin

, Volume 74, Issue 3, pp 98–107 | Cite as

Billiards and Integrability in Geometry and Physics. New Scope and New Potential

  • A. T. FomenkoEmail author
  • V. V. VedyushkinaEmail author
Article
  • 11 Downloads

Abstract

Description of bifurcations and symmetries of integrable systems is an important branch of geometry that has many applications. Important results have been obtained recently in the descriptions of bifurcations of integrable billiards and in modelling of Hamiltonian systems of mechanics and dynamics by billiards. The paper contains interesting problems, as well as a research program for the near future. In the closing of the paper, the results allowing one to describe hidden symmetries of Hamiltonian bifurcations are given as an example of a work close to billiards subject.

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Notes

Acknowledgments

The work was supported by the Program “Leading Scientific Schools” (project NSh-6399.2018.1, Agreement no. 075-02-2018-867) and by the Russian Foundation for Basic Research (project no. 16-01-00378-a).

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© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Faculty of Mechanics and MathematicsMoscow State UniversityLeninskie Gory, MoscowRussia

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