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 Regul. Chaotic Dyn., 2014, Volume 19, Issue 2, Pages 162–184 (Mi rcd108)

Systems of Kowalevski Type and Discriminantly Separable Polynomials

a Mathematical Institute SANU, Kneza Mihaila 36, 11000 Belgrade, Serbia
b The Department of Mathematical Sciences, University of Texas at Dallas, 800 West Campbell Road, Richardson TX 75080, USA
c Faculty for Traffic and Transport Engineering, University of Belgrade, Vojvode Stepe 305, 11000 Belgrade, Serbia

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

 Funding Agency Grant Number Serbian Ministry of Science and Technological Development 174020 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.

DOI: https://doi.org/10.1134/S1560354714020026

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Bibliographic databases:

Document Type: Article
MSC: 37J35, 37K60, 70E17, 70E40, 39A10
Accepted:09.11.2013
Language: English

Citation: Vladimir Dragović, Katarina Kukić, “Systems of Kowalevski Type and Discriminantly Separable Polynomials”, Regul. Chaotic Dyn., 19:2 (2014), 162–184

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/rcd108
• http://mi.mathnet.ru/eng/rcd/v19/i2/p162

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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. Dragovic, K. Kukic, “Discriminantly separable polynomials and quad-equations”, J. Geom. Mech., 6:3 (2014), 319–333
2. 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
3. P. E. Ryabov, A. Yu. Savushkin, “Fazovaya topologiya volchka Kovalevskoi – Sokolova”, Nelineinaya dinam., 11:2 (2015), 287–317
4. Mikhail P. Kharlamov, Pavel E. Ryabov, Alexander Yu. Savushkin, “Topological Atlas of the Kowalevski–Sokolov Top”, Regul. Chaotic Dyn., 21:1 (2016), 24–65
5. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Generalizations of the Kovalevskaya case and quaternions”, Proc. Steklov Inst. Math., 295 (2016), 33–44
6. V. Dragovic, K. Kukic, “Discriminantly separable polynomials and the generalized Kowalevski top”, Theor. Appl. Mech., 44:2 (2017), 229–236
7. Vladimir Dragović, Milena Radnović, “Caustics of Poncelet Polygons and Classical Extremal Polynomials”, Regul. Chaotic Dyn., 24:1 (2019), 1–35