Dynamics of generalized Poisson and Nambu–Poisson brackets

DOI10.1063/1.531960zbMath0878.58024OpenAlexW2077718370MaRDI QIDQ4345088

David Martín de Diego, Manuel de León, Juan Carlos Marrero, Raúl Ibáñez

Publication date: 15 January 1998

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.531960

zbMATH Keywords

Lagrangian submanifoldsPoisson bracketsPoisson morphismsNambu-Poisson bracketsgeneralized infinitesimal automorphisms

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45)

Related Items (14)

Poisson and integrable systems through the Nambu bracket and its Jacobi multiplier ⋮ On the \(N\)-extended Euler system: generalized Jacobi elliptic functions ⋮ Nambu structures on four-dimensional real Lie groups and related superintegrable systems ⋮ Geometric Hamilton–Jacobi theory on Nambu–Poisson manifolds ⋮ BEREZIN–TOEPLITZ QUANTIZATION, HYPERKÄHLER MANIFOLDS, AND MULTISYMPLECTIC MANIFOLDS ⋮ Multisymplectic structures induced by symplectic structures ⋮ On time-dependent Hamiltonian realizations of planar and nonplanar systems ⋮ On Deformations of n-Lie Algebras ⋮ On higher analogues of Courant algebroids ⋮ SUPERINTEGRABLE SYSTEMS, MULTI-HAMILTONIAN STRUCTURES AND NAMBU MECHANICS IN AN ARBITRARY DIMENSION ⋮ A geometric Hamilton–Jacobi theory on a Nambu–Jacobi manifold ⋮ Reduction of generalized Poisson and Nambu-Poisson manifolds ⋮ Jacobi structures in R3 ⋮ Tetraplectic structures, tri-momentum maps, and quaternionic flag manifolds

Cites Work

• Coisotropic calculus and Poisson groupoids
• On foundation of the generalized Nambu mechanics
• Some remarks concerning Nambu mechanics
• New generalized Poisson structures
• Tangent lifts of Poisson and related structures
• Generalized Hamiltonian Dynamics

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