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Lax representation and Poisson geometry of the Kowalevski top

TitleLax representation and Poisson geometry of the Kowalevski top
Publication TypeJournal Article
Year of Publication2001
AuthorsFalqui, G
JournalJ. Phys. A 34 (2001) 2077-2085
Abstract

We discuss the Poisson structure underlying the two-field Kowalevski gyrostat and the Kowalevski top. We start from their Lax structure and construct a suitable pencil of Poisson brackets which endows these systems with the structure of bi-Hamiltonian completely integrable systems. We study the Casimir functions of such pencils, and show how it is possible to frame the Kowalevski systems within the so-called Gel\\\'fand-Zakharevich bi-Hamiltonian setting for integrable systems.

URLhttp://hdl.handle.net/1963/3244
DOI10.1088/0305-4470/34/11/301

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