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Integrable Systems of Neumann Type

Dobrogowska, Alina ; Ratiu, Tudor

In: Journal of Dynamics and Differential Equations, 2015, vol. 27, no. 3-4, p. 533-553

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    Titre
    • Integrable Systems of Neumann Type
    Auteur
    • Dobrogowska, Alina. Section de Mathématiques, École Polytechnique Fédérale de Lausanne, 1015, Lausanne, Switzerland
    • Ratiu, Tudor. Section de Mathématiques and Bernoulli Center, École Polytechnique Fédérale de Lausanne, 1015, Lausanne, Switzerland
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Journal of Dynamics and Differential Equations, 2015, vol. 27, no. 3-4, p. 533-553. Springer US; http://www.springer-ny.com
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:331076
    Summary
    We construct families of integrable systems that interpolate between $$N$$ N -dimensional harmonic oscillators and Neumann systems. This is achieved by studying a family of integrable systems generated by the Casimir functions of the Lie algebra of real skew-symmetric matrices and a certain deformation thereof. Involution is proved directly, since the standard involution theorems do not apply to these families. It is also shown that the integrals are independent.