Skip to main content
SpringerLink
Log in

Maximally symmetric height atoms

  • Published:
Moscow University Mathematics Bulletin Aims and scope

Abstract

The concept of atom appearing first in the qualitative theory of dynamical systems finds its applications in many different branches of modern low-dimensional topology. Atoms are also of independent interest. In this paper we consider an important particular case of maximally symmetric atoms, so-called height maximally symmetric atoms which turn out to permit a simple description.

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. A. V. Bolsinov and A. T. Fomenko, Integrable Hamiltonian Systems, Vol. 1 (Udmurtskiy Univ., Izhevsk, 1999; CRC Press, Boca Raton, 2004).

    MATH  Google Scholar 

  2. A. T. Fomenko, “The Topology of Surfaces of Constant Energy in Integrable Hamiltonian Systems, and Obstructions to Integrability,” Izv. Akad. Nauk SSSR, Ser. Matem. 50(6), 1276 (1986) [Math. of the USSR-Izvestiya 29 (3), 629 (1987)].

    MathSciNet  MATH  Google Scholar 

  3. 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 

  4. A. T. Fomenko, “A Topological Invariant which Roughly Classifies Integrable Strictly Nondegenerate Hamiltonians on Four-Dimensional Symplectic Manifolds,” Funkts. Anal. Prilozhen. 25(4), 23 (1991) [Functional Anal. and Its Appl. 25 (4), 262 (1991)].

    MathSciNet  MATH  Google Scholar 

  5. V. O. Manturov, “Bifurcations, Atoms, and Knots,” Vestn. Mosk. Univ., Matem. Mekhan., No. 1, 3 (2000) [Moscow Univ. Math. Bull. 55 (1), 1 (2000)].

    Google Scholar 

  6. A. T. Fomenko, E. A. Kudryavtseva, and I. M. Nikonov, “Maximally Symmetric Cell Decompositions of Surfaces and Their Coverings,” Matem. Sborn. 199(9), 3 (2008) [Sbornik: Math. 199 (9), 1263 (2008)].

    Article  MathSciNet  Google Scholar 

  7. A. T. Fomenko, E. A. Kudryavtseva, and I. M. Nikonov, “Symmetric and Irreducible Abstract Polyhedra,” in Modern Problems of Mathematics and Mechanics, Ed. by A. T. Fomenko (Moscow State Univ., Moscow, 2009), pp. 58–97.

    Google Scholar 

  8. A. A. Oshemkov, “Morse Functions on Two-Dimensional Surfaces. Encoding Singularities,” Trudy Matem. Inst. Akad. Nauk SSSR 205, 131 (1994) [Proc. Steklov Inst. Math. 205, 119 (1995)].

    Google Scholar 

Download references

Author information

Authors and Affiliations

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

    I. M. Nikonov & N. V. Volchanetskii

Authors
  1. I. M. Nikonov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. V. Volchanetskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © I. M. Nikonov and N. V. Volchanetskii, 2013, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2013, Vol. 67, No. 2, pp. 3–6.

About this article

Cite this article

Nikonov, I.M., Volchanetskii, N.V. Maximally symmetric height atoms. Moscow Univ. Math. Bull. 68, 83–86 (2013). https://doi.org/10.3103/S0027132213020010

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0027132213020010

Keywords

Search

Navigation