Integrable systems, Poisson pencils, and hyperelliptic Lax pairs

DOI10.1007/BF02365199zbMath0985.37060MaRDI QIDQ5906417

Yuri N. Fedorov

Publication date: 29 September 1999

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/68776

zbMATH Keywords

Poisson bracketsLax pairintegrable Hamiltonian systemsClebsch-Perelomov systemhyperelliptic Laxintegrable Steklov-Lyapunov systemsL-A pairLie algebra so\((m)\)multidimensional Manakov system

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Dynamical systems in classical and celestial mechanics (37N05) Integrable cases of motion in rigid body dynamics (70E40) Higher-dimensional generalizations in rigid body dynamics (70E45)

Cites Work

• Geodesic flow on \(SO(4)\) and Abelian surfaces
• Some remarks on the integrability of the equations of motion of a rigid body in an ideal fluid
• Commutative families of functions related to consistent Poisson brackets
• A simple model of the integrable Hamiltonian equation
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