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Bogoyavlensky–Volterra and Birkhoff integrable systems

✍ Scribed by Pantelis A. Damianou; Stelios P. Kouzaris

Book ID
104085853
Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
194 KB
Volume
195
Category
Article
ISSN
0167-2789

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✦ Synopsis

In this paper we examine an interesting connection between the generalized Volterra lattices of Bogoyavlensky and a special case of an integrable system defined by Sklyanin. The Sklyanin system happens to be one of the cases in the classification of Kozlov and Treshchev of Birkhoff integrable Hamiltonian systems. Using this connection we demonstrate the integrability of the system and define a new Lax pair representation. In addition, we comment on the bi-Hamiltonian structure of the system.

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