On algebraic construction of certain integrable and super-integrable systems

DOI10.1016/j.physd.2011.05.020zbMath1223.37086arXiv1011.3249OpenAlexW1988544501WikidataQ104404796 ScholiaQ104404796MaRDI QIDQ720711

Maria Przybylska, Andrzej J. Maciejewski, Andreĭ Vladimirovich Tsyganov

Publication date: 11 October 2011

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.3249

zbMATH Keywords

Poisson manifoldhypergeometric functionseparation of variablesbi-Hamiltonian systemssuper-integrability

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30)

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Cites Work

• Unnamed Item
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• Necessary conditions for super-integrability of Hamiltonian systems
• On maximally superintegrable systems
• Darboux points and integrability of homogeneous Hamiltonian systems with three and more degrees of freedom
• Darboux points and integrability of homogeneous Hamiltonian systems with three and more degrees of freedom. Nongeneric cases
• Leonard Euler: addition theorems and superintegrable systems
• Superintegrable system on a sphere with the integral of higher degree
• Towards a classification of natural integrable systems
• Complex Euclidean super-integrable potentials, potentials of Drach, and potential of Holt
• Algebraic properties of master symmetries and their applications
• A note on the non-integrability of some Hamiltonian systems with a homogeneous potential.
• Symbolic software for separation of variables in the Hamilton-Jacobi equation for the \(L\)-systems
• All meromorphically integrable 2D Hamiltonian systems with homogeneous potential of degree 3
• On bi-Integrable Natural Hamiltonian Systems on Riemannian Manifolds
• Darboux points and integrability of Hamiltonian systems with homogeneous polynomial potential
• Unified treatment and classification of superintegrable systems with integrals quadratic in momenta on a two-dimensional manifold
• Polynomial Poisson algebras for classical superintegrable systems with a third-order integral of motion
• Addition theorems and the Drach superintegrable systems
• DIFFERENTIAL GALOIS THEORY AND INTEGRABILITY
• Differential Galois theory and non-integrability of Hamiltonian systems