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Nelin. Dinam., 2016, Volume 12, Number 4, Pages 633–650 (Mi nd543)  

This article is cited in 1 scientific paper (total in 1 paper)

Original papers

The discriminant set and bifurcation diagram of the integrable case of M. Adler and P. van Moerbeke

P. E. Ryabovabc, E. O. Biruchevad

a Moscow Institute of Physics and Technology (State University), Institutskiy per. 9, Dolgoprudny, Moscow Region, 141701, Russia
b Blagonravov Institute for Machine Science, Russian Academy of Sciences, ul.Bardina 4, Moscow, 119334, Russia
c Financial University under the Government of Russian Federation, Leningradsky pr. 49, Moscow, 125993, Russia
d Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991, Russia

Abstract: The paper presents explicitly the spectral curve and the discriminant set of the integrable case of M. Adler and P. van Moerbeke. For critical points of rank 0 and 1 of the momentum map we explicitly calculate the characteristic values defining their type. An algorithm is proposed for finding the bifurcation diagram from the real part of the discriminant set with the help of critical points of rank 0 and 1. The algorithm works under the condition that the real part of the discriminant set contains the bifurcation diagram.

Keywords: integrable Hamiltonian systems, spectral curve, discriminant set, bifurcation diagram

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00119
16-01-00170
15-41-02049


DOI: https://doi.org/10.20537/nd1604007

Full text: PDF file (364 kB)
References: PDF file   HTML file

UDC: 517.938.5+531.38
MSC: 70E05, 70E17, 37J35, 34A05
Received: 29.08.2016
Accepted:20.09.2016

Citation: P. E. Ryabov, E. O. Birucheva, “The discriminant set and bifurcation diagram of the integrable case of M. Adler and P. van Moerbeke”, Nelin. Dinam., 12:4 (2016), 633–650

Citation in format AMSBIB
\Bibitem{RyaBir16}
\by P.~E.~Ryabov, E.~O.~Birucheva
\paper The discriminant set and bifurcation diagram of the integrable case of M. Adler and P. van Moerbeke
\jour Nelin. Dinam.
\yr 2016
\vol 12
\issue 4
\pages 633--650
\mathnet{http://mi.mathnet.ru/nd543}
\crossref{https://doi.org/10.20537/nd1604007}
\elib{https://elibrary.ru/item.asp?id=27715768}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. V. Sokolov, “Integriruemyi sluchai Adlera–van Mërbeke. Vizualizatsiya bifurkatsii torov Liuvillya”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:4 (2017), 532–539  mathnet  crossref  elib
  • Нелинейная динамика
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