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Separation of variables for Bi-Hamiltonian systems

TitleSeparation of variables for Bi-Hamiltonian systems
Publication TypeJournal Article
Year of Publication2003
AuthorsFalqui, G, Pedroni, M
JournalMath. Phys. Anal. Geom. 6 (2003) 139-179

We address the problem of the separation of variables for the Hamilton-Jacobi equation within the theoretical scheme of bi-Hamiltonian geometry. We use the properties of a special class of bi-Hamiltonian manifolds, called omega-N manifolds, to give intrisic tests of separability (and Staeckel separability) for Hamiltonian systems. The separation variables are naturally associated with the geometrical structures of the omega-N manifold itself. We apply these results to bi-Hamiltonian systems of the Gel\\\'fand-Zakharevich type and we give explicit procedures to find the separated coordinates and the separation relations.


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