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Modeling Nondegenerate Bifurcations of Closures of Solutions for Integrable Systems with Two Degrees of Freedom by Integrable Topological Billiards

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Abstract

It is well known that surgeries of closures of solutions for integrable nondegenerate Hamiltonian systems with two degrees of freedom at a level of constant energy are classified by the so-called 3-atoms. These surgeries correspond to singular leaves of the Liouville foliation of three-dimensional isoenergetic surfaces. In this paper we prove the Fomenko conjecture that all such surgeries are modeled by integrable topological two-dimensional billiards (billiard books).

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Authors and Affiliations

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

    V. V. Vedyushkina, A. T. Fomenko & I. S. Kharcheva

Authors
  1. V. V. Vedyushkina
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  2. A. T. Fomenko
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  3. I. S. Kharcheva
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Correspondence to V. V. Vedyushkina.

Additional information

Original Russian Text © V.V. Vedyushkina, A.T. Fomenko, I.S. Kharcheva, 2018, published in Doklady Akademii Nauk, 2018, Vol. 479, No. 6, pp. 607–610.

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Vedyushkina, V.V., Fomenko, A.T. & Kharcheva, I.S. Modeling Nondegenerate Bifurcations of Closures of Solutions for Integrable Systems with Two Degrees of Freedom by Integrable Topological Billiards. Dokl. Math. 97, 174–176 (2018). https://doi.org/10.1134/S1064562418020230

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  • DOI: https://doi.org/10.1134/S1064562418020230

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