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Communication Dans Un Congrès Année : 2008

Hamiltonian systems on the "coupled" curves, Nambu-Poisson mechanics and Fairlie-type integrable systems

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T. Skrypnyk
  • Fonction : Auteur

Résumé

We consider some polynomial Poisson structures induced by Nambu brackets andHamiltonian systems associated with them. The case of Poisson brackets induced bythe canonical Nambu structure is discussed in details. We show that it provides ina natural way a Poisson structure on the product of the two algebraic curves. Weconsider explicitly several types of the integrable systems associated with such a con-struction. In particular we obtain the ”elegant” integrable system of Fairlie and itsvarious generalizations, two particle elliptic and ”double elliptic” Calogero system andtheir ’higher genus’ analogs.
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Dates et versions

hal-03031614 , version 1 (30-11-2020)

Identifiants

  • HAL Id : hal-03031614 , version 1
  • OKINA : ua67

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Vladimir Roubtsov, T. Skrypnyk. Hamiltonian systems on the "coupled" curves, Nambu-Poisson mechanics and Fairlie-type integrable systems. Travaux en cours en Physique Mathématiques, 2008, Non spécifié, France. ⟨hal-03031614⟩
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