Nonexistence of formal first integrals for general nonlinear systems under resonance

DOI10.1016/j.jmaa.2009.08.019zbMath1195.34008OpenAlexW2009392185MaRDI QIDQ1043917

Fang Liu, Shaoyun Shi, Zhi-Guo Xu

Publication date: 10 December 2009

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2009.08.019

zbMATH Keywords

nonintegrabilityfirst integralPoincaré-Dulac normal formsimple resonance

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (2)

Formal first integrals of general dynamical systems ⋮ Nonexistence of formal first integrals for nonlinear systems under the case of resonance

Cites Work

• Unnamed Item
• Branching of solutions and the nonexistence of first integrals in Hamiltonian mechanics. II
• Local first integrals of differential systems and diffeomorphisms
• On non-integrability of general systems of differential equations
• On the nonexistence of rational first integrals for systems of linear differential equations
• On the nonexistence of rational first integrals for nonlinear systems and semiquasihomogeneous systems
• Local first integrals for systems of differential equations
• Integrability, partial integrability, and nonintegrability for systems of ordinary differential equations
• Necessary condition for the existence of algebraic first integrals
• Non-integrability for general nonlinear systems

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