Abstract:
Starting from the notion of discriminantly separable polynomials of
degree two in each of three variables, we construct a class of
integrable dynamical systems. These systems can be integrated
explicitly in genus two theta-functions in a procedure which is
similar to the classical one for the Kowalevski top. The
discriminantly separable polynomials play the role of the Kowalevski
fundamental equation. Natural examples include the Sokolov
systems and the Jurdjevic elasticae.
Keywords:
integrable systems, Kowalevski top, discriminantly separable polynomials, systems of Kowalevski type.
The research was partially supported by the Serbian Ministry of Science and Technological Development, Project 174020 Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems.
Citation:
Vladimir Dragović, Katarina Kukić, “Systems of Kowalevski Type and Discriminantly Separable Polynomials”, Regul. Chaotic Dyn., 19:2 (2014), 162–184
\Bibitem{DraKuk14}
\by Vladimir~Dragovi\'c, Katarina~Kuki{\'c}
\paper Systems of Kowalevski Type and Discriminantly Separable Polynomials
\jour Regul. Chaotic Dyn.
\yr 2014
\vol 19
\issue 2
\pages 162--184
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Linking options:
https://www.mathnet.ru/eng/rcd108
https://www.mathnet.ru/eng/rcd/v19/i2/p162
This publication is cited in the following 13 articles:
Velimir Jurdjevic, “Integrable Systems: In the Footprints of the Greats”, Mathematics, 11:4 (2023), 1063
Jurdjevic V., “Kowalewski TOP and Complex Lie Algebras”, Anal. Math. Phys., 11:4 (2021), 173
Vladimir Dragović, Milena Radnović, “Caustics of Poncelet Polygons and Classical Extremal Polynomials”, Regul. Chaotic Dyn., 24:1 (2019), 1–35
Anani Komla Adabrah, Vladimir Dragović, Milena Radnović, “Periodic Billiards Within Conics in the Minkowski Plane and Akhiezer Polynomials”, Regul. Chaotic Dyn., 24:5 (2019), 464–501
V. M. Buchstaber, V. I. Dragovich, “Two-Valued Groups, Kummer Varieties, and Integrable Billiards”, Arnold Math. J., 4:1 (2018), 27–57
Vladimir Dragovich, Katarina Kukić, “Discriminantly separable polynomials and the generalized Kowalevski top”, Theor. Appl. Mech., 44:2 (2017), 229–236
Mikhail P. Kharlamov, Pavel E. Ryabov, Alexander Yu. Savushkin, “Topological Atlas of the Kowalevski–Sokolov Top”, Regul. Chaotic Dyn., 21:1 (2016), 24–65
I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Generalizations of the Kovalevskaya case and quaternions”, Proc. Steklov Inst. Math., 295 (2016), 33–44
Vladimir Dragović, Borislav Gajić, “Some Recent Generalizations of the Classical Rigid Body Systems”, Arnold Math J., 2:4 (2016), 511
P. E. Ryabov, A. Yu. Savushkin, “Fazovaya topologiya volchka Kovalevskoi – Sokolova”, Nelineinaya dinam., 11:2 (2015), 287–317
Vladimir Dragović, Katarina Kukić, Springer Proceedings in Physics, 163, Nonlinear Mathematical Physics and Natural Hazards, 2015, 49
V. Dragovic, K. Kukic, “Discriminantly separable polynomials and quad-equations”, J. Geom. Mech., 6:3 (2014), 319–333
V. Dragovic, K. Kukic, “Role of discriminantly separable polynomials in integrable dynamical systems”, Tim 2013 Physics Conference, AIP Conf. Proc., 1634, eds. O. Bunoiu, N. Avram, A. Popescu, Amer. Inst. Phys., 2014, 3–8
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