Poisson and Symplectic Structures, Hamiltonian Action, Momentum and Reduction

DOI10.1007/978-3-030-63253-3_1OpenAlexW3014470052MaRDI QIDQ5048597

Denys Dutykh, Vladimir Roubtsov

Publication date: 16 November 2022

Published in: Differential Geometry, Differential Equations, and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.14173

zbMATH Keywords

reductionPoisson bracketsPoisson manifoldsmomentum mapPoisson-Lie structuresPoisson bi-vectors

Mathematics Subject Classification ID

Introductory exposition (textbooks, tutorial papers, etc.) pertaining to differential geometry (53-01) Symplectic geometry, contact geometry (53Dxx) General theory of finite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, invariants (37J06) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Cites Work

• The local structure of Poisson manifolds
• Poisson Lie groups, dressing transformations, and Bruhat decompositions
• Poisson geometry
• Les variétés de Poisson et leurs algèbres de Lie associees
• Structure of dynamical systems. A symplectic view of physics. Transl. from the French by C. H. Cushman-de Vries. Transl. ed.: R. H. Cushman a. G. M. Tuynman
• THE STRUCTURES OF HAMILTONIAN MECHANICS
• Quantum groups
• Dressing transformations and Poisson group actions
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