N. N. Bogolyubov's functional equation and the Lie-Poisson-Vlasov symplectic structure associated with it
type: Item
instance of: scholarly article
title: N. N. Bogolyubov's functional equation and the Lie-Poisson-Vlasov symplectic structure associated with it
zbMATH Open document ID: 0625.58033
DOI: 10.1007/BF01056653
author: A. K. Prykarpats'kyi
author: Nikolai N. jun. Bogolubov
author: Valeriy H. Samoylenko
published in: Ukrainian Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: The authors show that Bogolyubov's functional equation is Hamiltonian relative to the Lie-Poisson bracket associated with a ``hierarchical'' Lie algebra which is used in the Hamiltonian description of the BBGKY equations.
reviewed by: T. S. Ratiu
Mathematics Subject Classification ID: 58Z05
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 34K99
zbMATH DE Number: 4015770
zbMATH Keywords: Poisson-Vlasov bracket
zbMATH Keywords: Hamiltonian structure
zbMATH Keywords: Bogolyubov's functional equation
zbMATH Keywords: Lie-Poisson bracket
MaRDI profile type: Publication
cites work: Q3696277
cites work: Q3261267
cites work: Q5842076
cites work: Q5662607
cites work: Canonical derivation of the Vlasov-Coulomb noncanonical Poisson structure
cites work: The moment map and collective motion
cites work: Canonical maps between semidirect products with applications to elasticity and superfluids
cites work: Kac-Moody Lie algebras and soliton equations. II: Lax equations associated with \(A_ 1^{(1)}\)
cites work: Q4725375
full work available at URL: https://doi.org/10.1007/bf01056653
OpenAlex ID: W2021398214
description: scientific article; zbMATH DE number 4015770