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Toda systems and exponents of simple Lie groups

✍ Scribed by Joana M. Nunes da Costa; Pantelis A. Damianou

Publisher
Elsevier Science
Year
2001
Tongue
French
Weight
113 KB
Volume
125
Category
Article
ISSN
0007-4497

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✦ Synopsis

Results on the finite nonperiodic A n Toda lattice are extended to the Bogoyavlesky Toda systems of type B n and C n . The areas investigated, include master symmetries, recursion operators, higher Poisson brackets and invariants. The results are presented both in Flaschka coordinates (a, b) as well as in the natural (q, p) coordinates. A conjecture which relates the degrees of higher Poisson brackets and the exponents of the corresponding Lie group is verified for these systems. © 2001 Éditions scientifiques et médicales Elsevier SAS RÉSUMÉ. -On étend des résultats sur le système Toda A n , fini et non-périodique, aux systèmes Toda de Bogoyavlesky de types B n et C n . Les sujets traités comprennent les master symmetries, les opérateurs de récursion, les crochets de Poisson et les invariants. Les résultats sont présentés en coordonnées (a, b) de Flaschka et aussi en coordonnées naturelles (q, p). Une conjecture qui met en rapport les degrés des crochets de Poisson avec les exponents des groupes de Lie qui leur correspondent est vérifiée pour ces systèmes.

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