Abstract
This chapter is devoted to the standard results of the algebraic theory of bi-Hamiltonian systems, developed during the last two decades. The crucial concepts like the one of the recursion operator introduced by Olver [158], the bi-Hamiltonian property formulated by Magri [123] as well as the hereditary property introduced by Fuchssteiner [82] gave a background for the modern algebraic theory of integrable systems.
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© 1998 Springer-Verlag Berlin Heidelberg
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Blaszak, M. (1998). The Theory of Hamiltonian and Bi-Hamiltonian Systems. In: Multi-Hamiltonian Theory of Dynamical Systems. Texts and Monographs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58893-8_3
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DOI: https://doi.org/10.1007/978-3-642-58893-8_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-63780-3
Online ISBN: 978-3-642-58893-8
eBook Packages: Springer Book Archive