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Elliptic curves and a new construction of integrable systems

Elliptic curves and a new construction of integrable systems 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Regular and Chaotic Dynamics Springer Journals

Elliptic curves and a new construction of integrable systems

Regular and Chaotic Dynamics , Volume 14 (5) – Aug 26, 2009

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References (24)

Publisher
Springer Journals
Copyright
Copyright © 2009 by Pleiades Publishing, Ltd.
Subject
Mathematics; Dynamical Systems and Ergodic Theory
ISSN
1560-3547
eISSN
1468-4845
DOI
10.1134/S1560354709040042
Publisher site
See Article on Publisher Site

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.

Journal

Regular and Chaotic DynamicsSpringer Journals

Published: Aug 26, 2009

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