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This article is cited in 35 scientific papers (total in 35 papers)
Compatible Poisson brackets on Lie algebras and completeness of families of functions in involution
A. V. Bolsinov
Abstract:
This paper presents a method for checking completeness of families of functions which are in involution with respect to compatible Poisson brackets. Several examples of compatible Poisson brackets on duals of Lie algebras are considered, as well as the associated involutive function families and Hamiltonian systems. The transitions of Liouville tori for some nonintegrable Hamiltonian systems, notably the equations of motion for a higher dimensional rigid body, are described.
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Mathematics of the USSR-Izvestiya, 1992, 38:1, 69–90
Bibliographic databases:
   
UDC:
513.944
MSC: 58F07
Received: 13.07.1989
Citation:
A. V. Bolsinov, “Compatible Poisson brackets on Lie algebras and completeness of families of functions in involution”, Izv. Akad. Nauk SSSR Ser. Mat., 55:1 (1991), 68–92; Math. USSR-Izv., 38:1 (1992), 69–90
Citation in format AMSBIB
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