Authors: Dragović, Vladimir 
Gajić, Borislav 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Elliptic curves and a new construction of integrable systems
Journal: Regular and Chaotic Dynamics
Volume: 14
Issue: 4-5
First page: 466
Last page: 478
Issue Date: 17-Sep-2009
Rank: M22
ISSN: 1560-3547
DOI: 10.1134/S1560354709040042
Abstract: 
A class of elliptic curves with associated Lax matrices is considered. A family of dynamical systems on e (3) parametrized by polynomial a with the above Lax matrices are constructed. Five cases from the family are selected by the condition of preserving the standard measure. Three of them are Hamiltonian. It is proved that two other cases are not Hamiltonian in the standard Poisson structure on e (3). Integrability of all five cases is proven. Integration procedures are performed in all five cases. Separation of variables in Sklyanin sense is also given. A connection with Hess-Appel-rot system is established. A sort of separation of variables is suggested for the Hess-Appel-rot system.
Keywords: Elliptic curves | Hess-Appel'rot system | Integrability | L-A pair | Separation of variables
Publisher: Springer Link
Project: Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems 

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