A Hamilton-Jacobi theory for general dynamical systems and integrability by quadratures in symplectic and Poisson manifolds

DOI10.1016/j.geomphys.2016.07.010zbMath1402.70018arXiv1512.03121OpenAlexW2191536833MaRDI QIDQ335808

Edith Padrón, Sergio Daniel Grillo

Publication date: 2 November 2016

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.03121

zbMATH Keywords

integrable systemsPoisson manifoldHamilton-Jacobi equations

Mathematics Subject Classification ID

Poisson manifolds; Poisson groupoids and algebroids (53D17) Hamilton-Jacobi equations in mechanics (70H20)

Related Items

Geometric Hamilton–Jacobi theory for systems with external forces, Non-commutative integrability, exact solvability and the Hamilton-Jacobi theory, On the geometry of the Hamilton-Jacobi equation and generating functions, Hamilton-Jacobi theory and integrability for autonomous and non-autonomous contact systems, Extended Hamilton–Jacobi theory, contact manifolds, and integrability by quadratures, Existence of isotropic complete solutions of the \(\Pi\)-Hamilton-Jacobi equation, Hamilton–Jacobi formalism on locally conformally symplectic manifolds, Reviewing the geometric Hamilton–Jacobi theory concerning Jacobi and Leibniz identities

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dynamics on Leibniz manifolds
• Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic mechanics
• Generalized Liouville method of integration of Hamiltonian systems
• Nonholonomic reduction
• On a generalization of the Hamilton-Jacobi method.
• On the Hamiltonian formulation of nonholonomic mechanical systems
• Algebroids -- general differential calculi on vector bundles
• Superintegrable Hamiltonian systems: Geometry and perturbations
• A Hamilton-Jacobi theory on Poisson manifolds
• The Hamilton-Jacobi equation, integrability, and nonholonomic systems
• Action-angle Coordinates for Integrable Systems on Poisson Manifolds
• GEOMETRIC HAMILTON–JACOBI THEORY
• Generalized nonholonomic mechanics, servomechanisms and related brackets
• GEOMETRIC HAMILTON–JACOBI THEORY FOR NONHOLONOMIC DYNAMICAL SYSTEMS
• A unified framework for mechanics: Hamilton–Jacobi equation and applications
• On global action-angle coordinates
• On almost-Poisson structures in nonholonomic mechanics