Non-integrability of ABC flow

DOI10.1016/S0375-9601(02)01259-8zbMath0999.37036WikidataQ104405077 ScholiaQ104405077MaRDI QIDQ1847724

Maria Przybylska, Andrzej J. Maciejewski

Publication date: 23 October 2002

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

zbMATH Keywords

meromorphic first integraldifferential galois theoryZiglin theory

Mathematics Subject Classification ID

Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30)

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Cites Work

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• The \(ABC\)-flow is not integrable for \(A=B\)
• Branching of solutions and the nonexistence of first integrals in Hamiltonian mechanics. II
• The absence of an additional real-analytic first integral in some problems of dynamics
• Nonintegrability of the Suslov problem
• Integrability and Non-Integrability of Planar Hamiltonian Systems of Cosmological Origin
• Nonintegrability of Bianchi VIII Hamiltonian system
• Chaotic streamlines in the ABC flows
• On the absence of a real-analytic first integral for ABC flow when A=B
• Chaotic and Resonant Streamlines in the ABC Flow
• Differential Galois theory and non-integrability of Hamiltonian systems