N. N. Bogolyubov's functional equation and the Lie-Poisson-Vlasov symplectic structure associated with it

DOI10.1007/BF01056653zbMath0625.58033OpenAlexW2021398214MaRDI QIDQ579711

Anatoliy K. Prykarpatsky, Nikolai N. jun. Bogoliubov, Valeriy H. Samoylenko

Publication date: 1986

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01056653

zbMATH Keywords

Hamiltonian structureLie-Poisson bracketBogolyubov's functional equationPoisson-Vlasov bracket

Mathematics Subject Classification ID

Applications of global analysis to the sciences (58Z05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Functional-differential equations (including equations with delayed, advanced or state-dependent argument) (34K99)

Cites Work

• Canonical maps between semidirect products with applications to elasticity and superfluids
• Kac-Moody Lie algebras and soliton equations. II: Lax equations associated with \(A_ 1^{(1)}\)
• The moment map and collective motion
• Canonical derivation of the Vlasov-Coulomb noncanonical Poisson structure
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