On a class of integrable systems with a cubic first integral

DOI10.1007/s00220-010-1107-7zbMath1206.37035OpenAlexW2502058716WikidataQ126126736 ScholiaQ126126736MaRDI QIDQ707590

Galliano Valent

Publication date: 8 October 2010

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00220-010-1107-7

zbMATH Keywords

linearizationintegrable systemcubic first integralrelevant metric

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Dynamical systems methods for problems in mechanics (70G60)

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On a class of integrable systems with a quartic first integral ⋮ Integrable cosmological potentials ⋮ First integrals of motion for two dimensional weight-homogeneous Hamiltonian systems in curved spaces ⋮ Integrability analysis of natural Hamiltonian systems in curved spaces ⋮ Open problems, questions and challenges in finite- dimensional integrable systems ⋮ Explicit metrics for a class of two-dimensional cubically superintegrable systems ⋮ On one integrable system with a cubic first integral ⋮ Two-dimensional superintegrable metrics with one linear and one cubic integral ⋮ Massless geodesics in \(\text{AdS}_5\times Y(p,q)\) as a superintegrable system ⋮ On two-dimensional integrable models with a cubic or quartic integral of motion ⋮ Global structure and geodesics for Koenigs superintegrable systems

Cites Work

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• New families of conservative systems on \(S^2\) possessing an integral of fourth degree in momenta
• New examples of integrable conservative systems on \(S^2\) and the case of Goryachev-Chaplygin
• On a family of integrable systems on S² with a cubic integral of motion
• The Maupertuis principle and geodesic flows on the sphere arising from integrable cases in the dynamics of a rigid body
• Two-dimensional geodesic flows having first integrals of higher degree

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