Darboux polynomials and first integrals of polynomial Hamiltonian systems

DOI10.1016/J.CNSNS.2022.106338WikidataQ114196474 ScholiaQ114196474MaRDI QIDQ6495299

Andrei Pranevich, Eduard V. Musafirov, Alexander Grin

Publication date: 30 April 2024

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

zbMATH Keywords

multiplicityintegrabilityfirst integralDarboux polynomialpolynomial Hamiltonian system

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 finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Cites Work

• First integrals and Darboux polynomials of natural polynomial Hamiltonian systems
• Integrability of dynamical systems: algebra and analysis
• Darboux theory of integrability in \(\mathbb C^n\) taking into account the multiplicity
• Darboux polynomials and first integrals of natural polynomial Hamiltonian systems
• Superintegrable Hamiltonian systems: Geometry and perturbations
• Invariant algebraic curves and conditions for a centre
• Centennial History of Hilbert's 16th Problem
• On the integrability of Hamiltonian systems with d degrees of freedom and homogenous polynomial potential of degree n
• On Poisson’s Theorem of Building First Integrals for Ordinary Differential Systems
• Darboux integrability of 2-dimensional Hamiltonian systems with homogenous potentials of degree 3
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