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- Superintegrable_Hamiltonian_system abstract "In mathematics, a superintegrable Hamiltonian system is a Hamiltonian system on a 2n-dimensional symplectic manifold for which the following conditions hold:(i) There exist n ≤ k independent integrals F i of motion. Their level surfaces (invariant submanifolds) form a fibered manifold over a connected open subset .(ii) There exist smooth real functions on such that the Poisson bracket of integrals of motion reads. (iii) The matrix function is of constant corank on .If , this is the case of a completely integrable Hamiltonian system. The Mishchenko-Fomenko theorem for superintegrable Hamiltonian systems generalizes the Liouville-Arnold theorem on action-angle coordinates of completely integrable Hamiltonian system as follows.Let invariant submanifolds of a superintegrable Hamiltonian system be connected compact and mutually diffeomorphic. Then the fibered manifold is a fiber bundlein tori . Given its fiber , there exists an open neighbourhood of which is a trivial fiber bundle provided with the bundle (generalized action-angle) coordinates ,, such that are coordinates on . These coordinates are the Darboux coordinates on a symplectic manifold . A Hamiltonian of a superintegrable system depends only on the action variables which are the Casimir functions of the coinduced Poisson structure on .The Liouville-Arnold theorem for completely integrable systems and the Mishchenko-Fomenko theorem for the superintegrable ones are generalized to the case of non-compact invariant submanifolds. They are diffeomorphic to a toroidal cylinder .".
- Superintegrable_Hamiltonian_system wikiPageExternalLink 1303.5363.
- Superintegrable_Hamiltonian_system wikiPageID "23655263".
- Superintegrable_Hamiltonian_system wikiPageRevisionID "550109275".
- Superintegrable_Hamiltonian_system hasPhotoCollection Superintegrable_Hamiltonian_system.
- Superintegrable_Hamiltonian_system subject Category:Dynamical_systems.
- Superintegrable_Hamiltonian_system subject Category:Hamiltonian_mechanics.
- Superintegrable_Hamiltonian_system type Abstraction100002137.
- Superintegrable_Hamiltonian_system type Attribute100024264.
- Superintegrable_Hamiltonian_system type DynamicalSystem106246361.
- Superintegrable_Hamiltonian_system type DynamicalSystems.
- Superintegrable_Hamiltonian_system type PhaseSpace100029114.
- Superintegrable_Hamiltonian_system type Space100028651.
- Superintegrable_Hamiltonian_system comment "In mathematics, a superintegrable Hamiltonian system is a Hamiltonian system on a 2n-dimensional symplectic manifold for which the following conditions hold:(i) There exist n ≤ k independent integrals F i of motion. Their level surfaces (invariant submanifolds) form a fibered manifold over a connected open subset .(ii) There exist smooth real functions on such that the Poisson bracket of integrals of motion reads.".
- Superintegrable_Hamiltonian_system label "Superintegrable Hamiltonian system".
- Superintegrable_Hamiltonian_system label "Суперинтегрируемая гамильтонова система".
- Superintegrable_Hamiltonian_system sameAs m.06zq2gn.
- Superintegrable_Hamiltonian_system sameAs Q7643453.
- Superintegrable_Hamiltonian_system sameAs Q7643453.
- Superintegrable_Hamiltonian_system sameAs Superintegrable_Hamiltonian_system.
- Superintegrable_Hamiltonian_system wasDerivedFrom Superintegrable_Hamiltonian_system?oldid=550109275.
- Superintegrable_Hamiltonian_system isPrimaryTopicOf Superintegrable_Hamiltonian_system.