Formal first integrals of general dynamical systems

DOI10.1155/2016/1036089zbMath1485.34008OpenAlexW2507638382WikidataQ59122186 ScholiaQ59122186MaRDI QIDQ310455

Qingjian Zhou, Jia Jiao, Wenlei Li

Publication date: 8 September 2016

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

Full work available at URL: https://doi.org/10.1155/2016/1036089

zbMATH Keywords

integrabilitycriteria for existence of formal integralsgeneral analytic nonlinear systems

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Explicit solutions, first integrals of ordinary differential equations (34A05) Invariant manifolds for ordinary differential equations (34C45)

Cites Work

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• Bifurcation of solutions and the nonexistence of first integrals in Hamiltonian mechanics. I
• Nonexistence of formal first integrals for general nonlinear systems under resonance
• Branching of solutions and the nonexistence of first integrals in Hamiltonian mechanics. II
• Applications of centre manifold theory
• On non-integrability of general systems of differential equations
• Algebraic conditions for a centre or a focus in some simple systems of arbitrary degree
• On the nonexistence of rational first integrals for nonlinear systems and semiquasihomogeneous systems
• Nonexistence of formal first integrals for nonlinear systems under the case of resonance
• Integrability, partial integrability, and nonintegrability for systems of ordinary differential equations
• Necessary condition for the existence of algebraic first integrals
• Differential Galois theory and non-integrability of Hamiltonian systems
• Non-integrability for general nonlinear systems

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