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Systems of Kowalevski type and discriminantly separable polynomials

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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.

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Authors and Affiliations

  1. The Department of Mathematical Sciences, University of Texas at Dallas, 800 West Campbell Road, Richardson, TX, 75080, USA

    Vladimir Dragović

  2. Mathematical Institute SANU, Kneza Mihaila 36, 11000, Belgrade, Serbia

    Vladimir Dragović

  3. Faculty for Traffic and Transport Engineering, University of Belgrade, Vojvode Stepe 305, 11000, Belgrade, Serbia

    Katarina Kukić

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  1. Vladimir Dragović
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  2. Katarina Kukić
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Correspondence to Vladimir Dragović.

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Dragović, V., Kukić, K. Systems of Kowalevski type and discriminantly separable polynomials. Regul. Chaot. Dyn. 19, 162–184 (2014). https://doi.org/10.1134/S1560354714020026

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

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