Abelian integrals, integrable dynamic systems of the Neumann-Rosochatius type, and the Lax representation

DOI10.1007/BF01058312zbMath0723.70012OpenAlexW1969323085MaRDI QIDQ757103

I. V. Mikityuk, Anatoliy K. Prykarpatsky, Valeriy H. Samoylenko

Publication date: 1989

Published in: Ukrainian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01058312

zbMATH Keywords

geodesic flowspectral problemsLax representationmultidimensional ellipsoidJacobi manifoldsalgebrogeometric descriptionclassical Hamiltonian system of Neumanncompletely integrable Hamiltonian dynamical systemsfinite-dimensional dynamical systems of oscillatory typeintegrability of dynamical systems of the Neumann-Rosochatius type

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Hamilton's equations (70H05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items (2)

Geometric quantization of Neumann-type completely integrable Hamiltonian systems ⋮ Algebraic structure of the gradient-holonomic algorithm for Lax integrable nonlinear dynamical systems. II. The reduction via Dirac and canonical quantization procedure

Cites Work

• Abelian integrals and the reduction method for an integrable Hamiltonian system
• Unnamed Item
• Unnamed Item

This page was built for publication: Abelian integrals, integrable dynamic systems of the Neumann-Rosochatius type, and the Lax representation