Abstract
We consider a dual space to a Lie algebra of deformed skew-symmetric matrices equipped with two compatible Poisson brackets: the Lie–Poisson bracket and the frozen bracket.We obtain a bi-Hamiltonian integrable system. As an example we present a case of a system on a two-dimensional quadric which can be seen as a generalization of the Neumann system.
Mathematics Subject Classification (2010). 37J35, 17B80, 53D17.
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© 2015 Springer International Publishing Switzerland
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Dobrogowska, A., Goliński, T. (2015). Examples of Hamiltonian Systems on the Space of Deformed Skew-symmetric Matrices. In: Kielanowski, P., Bieliavsky, P., Odzijewicz, A., Schlichenmaier, M., Voronov, T. (eds) Geometric Methods in Physics. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-18212-4_19
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DOI: https://doi.org/10.1007/978-3-319-18212-4_19
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-18211-7
Online ISBN: 978-3-319-18212-4
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