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Regul. Chaotic Dyn., 2005, Volume 10, Issue 1, Pages 59–70 (Mi rcd696)  

This article is cited in 8 scientific papers (total in 8 papers)

Separation of variables on a non-hyperelliptic curve

V. G. Marikhin, V. V. Sokolov

Landau Institute for Theoretical Physics, 2, Kosygina str., 119334 Moscow, Russia

Abstract: In the paper we consider several dynamical systems that admit a separation of variables on the algebraic curve of genus 4. The main result of the paper is an explicit formula for the action of these systems. It is obtained directly from the Hamilton–Jacobi equation. We find the action and a separation of variables for the Clebsch and the $so(4)$ Schottky–Manakov spinning tops.

Keywords: integrable tops, separation of variables, Hamilton–Jacobi equation

DOI: https://doi.org/10.1070/RD2005v010n01ABEH000300


Bibliographic databases:

MSC: 37N15, 37K20, 14K20
Received: 11.01.2005
Accepted:25.03.2005
Language:

Citation: V. G. Marikhin, V. V. Sokolov, “Separation of variables on a non-hyperelliptic curve”, Regul. Chaotic Dyn., 10:1 (2005), 59–70

Citation in format AMSBIB
\Bibitem{MarSok05}
\by V. G. Marikhin, V. V. Sokolov
\paper Separation of variables on a non-hyperelliptic curve
\jour Regul. Chaotic Dyn.
\yr 2005
\vol 10
\issue 1
\pages 59--70
\mathnet{http://mi.mathnet.ru/rcd696}
\crossref{https://doi.org/10.1070/RD2005v010n01ABEH000300}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2136830}
\zmath{https://zbmath.org/?q=an:1077.37518}


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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. V. G. Marikhin, V. V. Sokolov, “On quasi-Stäckel Hamiltonians”, Russian Math. Surveys, 60:5 (2005), 981–983  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. V. G. Marikhin, V. V. Sokolov, “Pairs of commuting Hamiltonians quadratic in the momenta”, Theoret. and Math. Phys., 149:2 (2006), 1425–1436  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. Gregorio Falqui, “A Note on the Rotationally Symmetric $\mathrm{SO}(4)$ Euler Rigid Body”, SIGMA, 3 (2007), 032, 13 pp.  mathnet  crossref  mathscinet  zmath
    4. M. P. Kharlamov, “Topologicheskii analiz i bulevy funktsii: I. Metody i prilozheniya k klassicheskim sistemam”, Nelineinaya dinam., 6:4 (2010), 769–805  mathnet
    5. V. E. Adler, V. G. Marikhin, A. B. Shabat, “Quantum tops as examples of commuting differential operators”, Theoret. and Math. Phys., 172:3 (2012), 1187–1205  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    6. A. V. Bolsinov, A. V. Borisov, I. S. Mamaev, “Geometrizatsiya teoremy Chaplygina o privodyaschem mnozhitele”, Nelineinaya dinam., 9:4 (2013), 627–640  mathnet
    7. Ivan A. Bizyaev, Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “Integrability and Nonintegrability of Sub-Riemannian Geodesic Flows on Carnot Groups”, Regul. Chaotic Dyn., 21:6 (2016), 759–774  mathnet  crossref  mathscinet
    8. Borisov A. Mamaev I., “Rigid Body Dynamics”, Rigid Body Dynamics, de Gruyter Studies in Mathematical Physics, 52, Walter de Gruyter Gmbh, 2019, 1–520  mathscinet  isi
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