Discriminantly Separable Polynomials and Their Applications

Dragović, Vladimir; Kukić, Katarina

doi:10.1007/978-3-319-14328-6_4

Cited by 1 publication

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“…If a system satisfies the above assumptions we will call it a system of the Kowalevski type. As it has been pointed out in the Introduction, see formulae (7,10,11,12), the Kowalevski top is an example of the systems of the Kowalevski type.…”

Section: Fundamental Steps In the Kowalevski Integration Proceduresmentioning

confidence: 98%

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Systems of Kowalevski type and discriminantly separable polynomials

Dragović

Kukić

2014

Regul. Chaot. Dyn.

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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 discriminnatly separable polynomials play the role of the Kowalevski fundamental equation. The natural examples include the Sokolov systems and the Jurdjevic elasticae.A partir de la notion des polynômes avec les discriminants séparables qui sont du second degré par rapport chacune de trois variables, nous construisons une classe des systemes dynamiques. On peut résoudre explicitement ces systemes via les fonctions thêta de genre 2, par une procédure similaire cette classique pour la toupie de Kowalevski. Les polynômes avec les discriminants séparables jouent le rôle de l'équation fondamentale de Kowalevski. Les exemples naturels incluent les systemes de Sokolov et leś elastiques de Jurdjevic.

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Section: Fundamental Steps In the Kowalevski Integration Proceduresmentioning

confidence: 98%

“…Referring to this question, we have already constructed discrete integrable systems related to discriminantly separable polynomials which are associated to quad-graphs in [11]. Now we are constructing a new class of integrable continuous systems, generalizing the Kowalevski top.…”

Section: A Short Note On Discriminantly Separable Polynomialsmentioning

confidence: 99%