Darboux integrability of generalized Yang–Mills Hamiltonian system

DOI10.1080/14029251.2016.1175820zbMath1420.37037OpenAlexW2325925395MaRDI QIDQ5231024

Claudia Valls, Jaume Llibre

Publication date: 29 August 2019

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/14029251.2016.1175820

zbMATH Keywords

Hamiltonian systemspolynomial integrabilityweight-homogenous differential systems

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30)

Related Items (9)

Darboux integrability of the simple chaotic flow with a line equilibria differential system ⋮ Detecting Order and Chaos by the mLE, SALI and GALI Methods in Three-Dimensional Nonlinear Yang–Mills System ⋮ Painlevé analysis and integrability of the trapped ionic system ⋮ Darboux and analytic integrability of five‐dimensional semiclassical Jaynes–Cummings system ⋮ The physics and applications of strongly coupled Coulomb systems (plasmas) levitated in electrodynamic traps ⋮ Kovalevskaya exponents, weak Painlevé property and integrability for quasi-homogeneous differential systems ⋮ On the Darboux integrability of a three–dimensional forced–damped differential system ⋮ Meromorphic and formal first integrals for the Lorenz system ⋮ Classical and quantum integrability of the three-dimensional generalized trapped ion Hamiltonian

Cites Work

• Multiplicity of invariant algebraic curves in polynomial vector fields
• Darboux theory of integrability for polynomial vector fields in taking into account the multiplicity at infinity
• Picard-Vessiot theory and Ziglin's theorem
• Non-integrability of generalized Yang-Mills Hamiltonian system
• Generalized separability for a Hamiltonian with nonseparable quartic potential
• Qualitative theory of planar differential systems
• Polynomial first integrals for quasi-homogeneous polynomial differential systems
• Singular point analysis and integrals of motion for coupled nonlinear Schrödinger equations
• Integrability of Hamiltonian systems and differential Galois groups of higher variational equations
• Analytic integrability of Hamiltonian systems with a homogeneous polynomial potential of degree 4
• Differential Galois theory and non-integrability of Hamiltonian systems

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