This article is cited in 14 papers

Systems of Kowalevski Type and Discriminantly Separable Polynomials

Vladimir Dragović^ab, Katarina Kukić<sup>c

a</sup> 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.

MSC: 37J35, 37K60, 70E17, 70E40, 39A10

Received: 30.08.2013
Accepted: 09.11.2013

Language: English

DOI: 10.1134/S1560354714020026

Bibliographic databases:

• 
• 
• 
•