Abstract:
We discuss the polynomial bi-Hamiltonian structures for the Kowalevski top in special case of zero square integral. An explicit procedure to find variables of separation and separation relations is considered in detail.
\Bibitem{Tsi10}
\by A. V. Tsiganov
\paper New variables of separation for particular case of the Kowalevski top
\jour Regul. Chaotic Dyn.
\yr 2010
\vol 15
\issue 6
\pages 659--669
\mathnet{http://mi.mathnet.ru/rcd525}
\crossref{https://doi.org/10.1134/S156035471006002X}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2747176}
\zmath{https://zbmath.org/?q=an:1258.70012}
Linking options:
https://www.mathnet.ru/eng/rcd525
https://www.mathnet.ru/eng/rcd/v15/i6/p659
This publication is cited in the following 13 articles:
Jurdjevic V., “Kowalewski TOP and Complex Lie Algebras”, Anal. Math. Phys., 11:4 (2021), 173
Andrey V. Tsiganov, “Simultaneous Separation for the Neumann and Chaplygin Systems”, Regul. Chaotic Dyn., 20:1 (2015), 74–93
V. A. Khudobakhshov, A. P. Sozonov, “Razdelenie peremennykh dlya odnogo obobscheniya volchka Kovalevskoi”, Nelineinaya dinam., 9:2 (2013), 247–255
Yu. A. Grigor'ev, V. A. Khudobakhshov, A. V. Tsiganov, “Separation of variables for some systems with a fourth-order integral of motion”, Theoret. and Math. Phys., 177:3 (2013), 1680–1692
Andrey V. Tsiganov, “New variables of separation for the Steklov–Lyapunov system”, SIGMA, 8 (2012), 012, 14 pp.
Andrey V. Tsiganov, “One Invariant Measure and Different Poisson Brackets for Two Non-Holonomic Systems”, Regul. Chaotic Dyn., 17:1 (2012), 72–96
V. A. Khudobakhshov, A. V. Tsyganov, “O kvadraturakh integriruemykh sistem na sfere s integralami dvizheniya starshikh stepenei”, Nelineinaya dinam., 7:1 (2011), 53–74
A. V. Tsyganov, “Deformatsii kanonicheskoi skobki Puassona dlya negolonomnykh sistem Chaplygina i Borisova–Mamaeva–Fëdorova pri nulevoi konstante ploschadei. I”, Nelineinaya dinam., 7:3 (2011), 577–599
Yu A Grigoryev, A V Tsiganov, “Separation of variables for the generalized Henon–Heiles system and system with quartic potential”, J. Phys. A: Math. Theor., 44:25 (2011), 255202
Andrey Tsiganov, “Integrable Euler top and nonholonomic Chaplygin ball”, Journal of Geometric Mechanics, 3:3 (2011), 337
Andrey V. Tsiganov, Vitaly A. Khudobakhshov, “Integrable Systems on the Sphere Associated with Genus Three Algebraic Curves”, Regul. Chaotic Dyn., 16:3 (2011), 396–414
A V Tsiganov, “On natural Poisson bivectors on the sphere”, J. Phys. A: Math. Theor., 44:10 (2011), 105203
A. V. Vershilov, “On the bi-Hamiltonian structure of Bogoyavlensky system on so(4)”, Regul. Chaotic Dyn., 15:6 (2010), 670–676
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