Integrability of Hamiltonian systems with algebraic potentials

DOI10.1016/j.physleta.2015.08.035zbMath1377.37097OpenAlexW1237724740WikidataQ104404649 ScholiaQ104404649MaRDI QIDQ1691001

Andrzej J. Maciejewski, Maria Przybylska

Publication date: 12 January 2018

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physleta.2015.08.035

zbMATH Keywords

integrabilityHamiltonian systemsdifferential Galois theorynon-integrability criteriaalgebraic potentials

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30)

Related Items

On superintegrable systems separable in Cartesian coordinates, Anisotropic Kepler and anisotropic two fixed centres problems, Integrability analysis of chaotic and hyperchaotic finance systems, Non-integrability of the planar elliptic restricted three-body problem, Non-integrability of the Kepler and the two-body problems on the Heisenberg group, Non-integrability of the spacial \(n\)-center problem

Cites Work

• Unnamed Item
• Unnamed Item
• Integrability of Hamiltonian systems with homogeneous potentials of degrees \(\pm 2\). An application of higher order variational equations
• Integrability of potentials of degree \(k \neq \pm 2\). Second order variational equations between Kolchin solvability and abelianity
• Bifurcation of solutions and the nonexistence of first integrals in Hamiltonian mechanics. I
• Multiparticle systems. The algebra of integrals and integrable cases
• Branching of solutions and the nonexistence of first integrals in Hamiltonian mechanics. II
• A criterion for the non-existence of an additional integral in Hamiltonian systems with a homogeneous potential
• A note on the non-integrability of some Hamiltonian systems with a homogeneous potential.
• Non-integrability of the generalized two fixed centres problem
• A note on algebraic potentials and Morales-Ramis theory
• Higher-order superintegrability of a Holt related potential
• Third order integrability conditions for homogeneous potentials of degree −1
• A nonseparable quantum superintegrable system in 2D real Euclidean space
• Integrability of Hamiltonian systems and differential Galois groups of higher variational equations
• Integrability conditions at order 2 for homogeneous potentials of degree −1
• Differential Galois theory and non-integrability of Hamiltonian systems