A review on coisotropic reduction in symplectic, cosymplectic, contact and co-contact Hamiltonian systems

DOI10.1088/1751-8121/ad37b2zbMATH Open1548.37084MaRDI QIDQ6561826

Rubén Izquierdo-López, Manuel de León

Publication date: 25 June 2024

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

zbMATH Keywords

symplectic manifoldsHamiltonian dynamicscontact manifoldscosymplectic manifoldscoisotropic reductioncocontact manifolds

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Contact manifolds (general theory) (53D10) Lagrangian submanifolds; Maslov index (53D12) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Contact systems (37J55) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Cites Work

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• Hamilton-Jacobi theory, symmetries and coisotropic reduction
• Contact symmetries and Hamiltonian thermodynamics
• Le théorème de réduction de Marsden-Weinstein en géométrie cosymplectique et de contact. (The Marsden-Weinstein reduction theorem in cosymplectic and contact geometry)
• Reduction and quantization for singular momentum mappings
• Contact structure in thermodynamic theory
• Reduction of symplectic manifolds with symmetry
• Continuous contact transformations in thermodynamics
• 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
• Rigidity of integral coisotropic submanifolds of contact manifolds
• Stable Hamiltonian structure and basic cohomology
• Optimal control, contact dynamics and Herglotz variational problem
• Symplectic manifolds and their Lagrangian submanifolds
• Hamilton-Jacobi theory and integrability for autonomous and non-autonomous contact systems
• A Tulczyjew triple for classical fields
• Methods of Differential Geometry in Classical Field Theories
• Time-dependent mechanics and Lagrangian submanifolds of presymplectic and Poisson manifolds
• Contact reduction
• Reduction, symmetry, and phases in mechanics
• GEOMETRIC HAMILTON–JACOBI THEORY
• On Coisotropic Imbeddings of Presymplectic Manifolds
• Lectures on Mechanics
• Gradient vector fields on cosymplectic manifolds
• Accessible Sets, Orbits, and Foliations with Singularities
• Reduction of Jacobi manifolds
• Co-isotropic and Legendre - Lagrangian submanifolds and conformal Jacobi morphisms
• Cosymplectic reduction for singular momentum maps
• Coisotropic regularization of singular Lagrangians
• The Geometry of Some Thermodynamic Systems
• Contact geometry for simple thermodynamical systems with friction
• Orbits of Families of Vector Fields and Integrability of Distributions
• Contact Hamiltonian systems
• Contact geometry and thermodynamics
• Tulczyjew's Triplet for Lie Groups II: Dynamics
• POISSON GEOMETRY IN CONSTRAINED SYSTEMS
• Quantization and unitary representations
• Functions Whose Poisson Brackets Are Constants
• Generalized Hamiltonian Dynamics
• Reviewing the geometric Hamilton–Jacobi theory concerning Jacobi and Leibniz identities
• Time-dependent contact mechanics

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