Skip to main content
SpringerLink
Log in

Fomenko–Zieschang Invariants of Topological Billiards Bounded by Confocal Parabolas

  • Published:
Moscow University Mathematics Bulletin Aims and scope

Abstract

A topological (Liouville) classification of integrable billiards in locally flat compact domains bounded by arcs of confocal parabolas is obtained by methods of Fomenko–Zieschang invariants of integrable systems theory.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. G. D. Birkhoff, Dynamical Systems (Publ. House “Udmurtskii Universitet,” Izhevsk, 1999; AMS, Providence, RI, 1927).

    Google Scholar 

  2. V. V. Kozlov and D. V. Treshchev, Billiards: A Genetic Introduction to the Dynamics of Systems with Impacts (Moscow State Univ., Moscow, 1991; in series: Translations of Math. Monographs, Vol. 89, Amer. Math. Soc., Providence, RI: 1991).

    Google Scholar 

  3. V. V. Fokicheva, “Classification of Billiard Motions in Domains Bounded by Confocal Parabolas,” Matem. Sbornik 205 (8), 139 (2014) [Sbornik Math. 205 (8) 1201 (2014)].

    Article  MathSciNet  MATH  Google Scholar 

  4. A. V. Bolsinov and A. T. Fomenko, Integrable Hamiltonian Systems. Geometry, Topology and Classification, Vol. 1, 2, (Publ. House “Udmurtskii Universitet,” Izhevsk, 1999; CRC Press, Boca Raton, FL, 2004).

    Google Scholar 

  5. A. T. Fomenko and H. Zieschang, “On Typical Topological Properties of Integrable Hamiltonian Systems,” Izvestiya Akad. Nauk SSSR 52 (2), 378 (1988) [Math. of the USSR–Izvestiya 32 (2), 385 (1989)].

    MATH  Google Scholar 

  6. A. T. Fomenko, “The Symplectic Topology of Completely Integrable Hamiltonian Systems,” Uspekhi Matem. Nauk 44 (1), 145 (1989) [Russian Math. Surveys 44 (1), 181 (1989)].

    MathSciNet  MATH  Google Scholar 

  7. A. T. Fomenko and H. Zieschang, “A Topological Invariant and a Criterion for the Equivalence of Integrable Hamiltonian Systems with Two Degrees of Freedom,” Izvestiya Akad. Nauk SSSR, Ser. Matem. 54 (3), 546 (1990) [Math. of the USSR–Izvestiya 36 (3), 567 (1991)].

    MathSciNet  MATH  Google Scholar 

  8. V. V. Fokicheva, “Description of Singularities for Billiard Systems Bounded by Confocal Ellipses or Hyperbolas,” Vestn. Mosk. Univ., Matem. Mekhan., No. 4, 18 (2014) [Moscow Univ. Math. Bulletin 69 (4), 148 (2014)].

    MathSciNet  MATH  Google Scholar 

  9. V. V. Fokicheva, “A Topological Classification of Billiards in Locally Planar Domains Bounded by Arcs of Confocal Quadrics,” Matem. Sbornik 206 (10), 127 (2015) [Sbornik Math. 206 (10), 1463 (2015)].

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, Moscow, 119991, Russia

    V. V. Vedyushkina

Authors
  1. V. V. Vedyushkina
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. V. Vedyushkina.

Additional information

Original Russian Text © V.V. Vedyushkina, 2018, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2018, Vol. 73, No. 4, pp. 22–28.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vedyushkina, V.V. Fomenko–Zieschang Invariants of Topological Billiards Bounded by Confocal Parabolas. Moscow Univ. Math. Bull. 73, 150–155 (2018). https://doi.org/10.3103/S0027132218040046

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0027132218040046

Search

Navigation