Completely integrable bi-Hamiltonian systems
From MaRDI portal
Publication:1319925
DOI10.1007/BF02219188zbMath0796.58020MaRDI QIDQ1319925
Publication date: 19 April 1994
Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)
Related Items
$3D$-flows generated by the curl of a vector potential & Maurer-Cartan equations, Multi-Hamiltonian structures for a class of degenerate completely integrable systems, Superintegrable cases of four-dimensional dynamical systems, Generically, Arnold-Liouville systems cannot be bi-Hamiltonian, Theory of tensor invariants of integrable Hamiltonian systems. I: Incompatible Poisson structures, Quasi-bi-Hamiltonian structures, complex functions and superintegrability: the Tremblay–Turbiner–Winternitz (TTW) and the Post–Winternitz (PW) systems, Tangent lifts of bi-Hamiltonian structures, Quasi-bi-Hamiltonian structures of the 2-dimensional Kepler problem, On a class of dynamical systems both quasi-bi-Hamiltonian and bi-Hamiltonian., Hamiltonian Dynamics for the Kepler Problem in a Deformed Phase Space, Quasi-bi-Hamiltonian structures and superintegrability: study of a Kepler-related family of systems endowed with generalized Runge-Lenz integrals of motion, On time-dependent Hamiltonian realizations of planar and nonplanar systems, Magri–Morosi–Gel’fand–Dorfman’s bi-Hamiltonian constructions in the action-angle variables, A Poisson structure on compact symmetric spaces, Dirac submanifolds and Poisson involutions, Generalization of the concept of classical \(r\)-matrix to Lie algebroids, Topology of the space of locally separable functions, About the separability of completely integrable quasi-bi-Hamiltonian systems with compact levels, Noncommutative Kepler dynamics: symmetry groups and bi-Hamiltonian structures, Bi-Hamiltonian structure of the bi-dimensional superintegrable nonlinear isotonic oscillator, On integrals, Hamiltonian and metriplectic formulations of polynomial systems in 3D, Bi-Hamiltonian manifolds, quasi-bi-Hamiltonian systems and separation variables, The action-angle coordinates revisited: bi-Hamiltonian systems, Compatibility of symplectic structures adapted to noncommutatively integrable systems, Separability of the Toda lattice, Master integrals, superintegrability and quadratic algebras
Cites Work
- The inverse problem in the calculus of variations and the geometry of the tangent bundle
- The local structure of Poisson manifolds
- The Kowalewski top 99 years later: a Lax pair, generalizations and explicit solutions
- R-matrices and higher Poisson brackets for integrable systems
- A simple model of the integrable Hamiltonian equation
- Unnamed Item
- Unnamed Item
- Unnamed Item
