On Extensions, Lie-Poisson Systems, and Dissipations

zbMath1495.37050arXiv2101.03951MaRDI QIDQ5065102

Serkan Sütlü, Oğul Esen, Gökhan Özcan

Publication date: 18 March 2022

Full work available at URL: https://arxiv.org/abs/2101.03951

zbMATH Keywords

unified productLie-Poisson equationmetriplectic system

Mathematics Subject Classification ID

Poisson manifolds; Poisson groupoids and algebroids (53D17) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) 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 Lie algebras and other algebraic structures (37J37)

Related Items

On geometry of multiscale mass action law and its fluctuations

Uses Software

• GENERIC

Cites Work

• Lagrangian dynamics on matched pairs
• Formulation of thermoelastic dissipative material behavior using GENERIC
• Metriplectic framework for dissipative magneto-hydrodynamics
• Vlasov moments, integrable systems and singular solutions
• Dynamics on Leibniz manifolds
• The local structure of Poisson manifolds
• Geometry of Vlasov kinetic moments: a bosonic Fock space for the symmetric Schouten bracket
• Extending structures. I: The level of groups.
• Extensions of Poisson algebras by derivations
• Metriplectic structure, Leibniz dynamics and dissipative systems
• Physics for algebraists: Non-commutative and non-cocommutative Hopf algebras by a bicrossproduct construction
• Double cross biproduct and bi-cycle bicrossproduct Lie bialgebras
• The Hamiltonian structure of the Maxwell-Vlasov equations
• Lie groups and algebras with applications to physics, geometry, and mechanics
• A paradigm for joined Hamiltonian and dissipative systems
• Poisson Lie groups, dressing transformations, and Bruhat decompositions
• Lie coalgebras
• Matched pairs of Lie groups associated to solutions of the Yang-Baxter equations
• The Euler-Poincaré equations and semidirect products with applications to continuum theories
• Symplectic reduction for semidirect products and central extensions
• Lectures on the geometry of Poisson manifolds
• Moment closure hierarchies for kinetic theories.
• Hamiltonian coupling of electromagnetic field and matter
• The Euler-Poincaré equations and double bracket dissipation
• Geometry of plasma dynamics. II: Lie algebra of Hamiltonian vector fields
• Classification and Casimir invariants of Lie-Poisson brackets
• Second order Lagrangian dynamics on double cross product groups
• Matched pair analysis of the Vlasov plasma
• Extending structures for Lie algebras
• Poisson structures and their normal forms
• Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems
• Lagrangian reduction by stages
• THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
• A geometric theory of selective decay with applications in MHD
• Multiscale Thermo-Dynamics
• Hamiltonian dynamics on matched pairs
• Corrigendum: Hamiltonian closures for fluid models with four moments by dimensional analysis (2015J. Phys. A: Math. Theor.48 275501)
• Higher moments for kinetic equations: The Vlasov-Poisson and Fokker-Planck cases
• Semidirect Products and Reduction in Mechanics
• Noncanonical Hamiltonian field theory and reduced MHD
• The Schouten - Nijenhuis bracket, cohomology and generalized Poisson structures
• Universal Central Extension of the Lie Algebra of Hamiltonian Vector Fields: Table 1.
• Extremal energy properties and construction of stable solutions of the Euler equations
• Gradient Flows in the Normal and Kähler Metrics and Triple Bracket Generated Metriplectic Systems
• Geometry of plasma dynamics. I. Group of canonical diffeomorphisms
• Single and double generator bracket formulations of multicomponent fluids with irreversible processes
• The twisted top
• Conformal Hamiltonian systems
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item