Integrable systems on the sphere associated with genus three algebraic curves

DOI10.1134/S1560354711030117zbMath1252.70041arXiv1109.1629OpenAlexW2055863192MaRDI QIDQ691187

Vitaly A. Khudobakhshov, Andreĭ Vladimirovich Tsyganov

Publication date: 30 November 2012

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.1629

zbMATH Keywords

integrable systemsseparation of variablesAbel equations

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Hamilton-Jacobi equations in mechanics (70H20)

Related Items (4)

Integrable systems on a sphere, an ellipsoid and a hyperboloid ⋮ Separation of variables for some systems with a fourth-order integral of motion ⋮ Abel's theorem and Bäcklund transformations for the Hamilton-Jacobi equations ⋮ Simultaneous separation for the Neumann and Chaplygin systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• New integrable systems with a quartic integral and new generalizations of kovalevskaya's and goriatchev's cases
• On one integrable system with a cubic first integral
• Classical integrable systems and billiards related to generalized Jacobians
• A new integrable system on the sphere
• On the Steklov-Lyapunov case of the rigid body motion
• Symbolic software for separation of variables in the Hamilton-Jacobi equation for the \(L\)-systems
• New variables of separation for particular case of the Kowalevski top
• On the generalized Chaplygin system
• On bi-Integrable Natural Hamiltonian Systems on Riemannian Manifolds
• On natural Poisson bivectors on the sphere
• On bi-Hamiltonian geometry of some integrable systems on the sphere with cubic integral of motion
• On the Kowalevski-Goryachev-Chaplygin gyrostat
• Simultaneous separation for the Kowalevski and Goryachev$ndash$Chaplygin gyrostats
• Poisson maps and integrable deformations of the Kowalevski top
• On a family of integrable systems on S² with a cubic integral of motion
• On two different bi-Hamiltonian structures for the Toda lattice

This page was built for publication: Integrable systems on the sphere associated with genus three algebraic curves