A note on the first integrals of the ABC system

DOI10.1063/1.3682692zbMath1274.76157OpenAlexW1971918470MaRDI QIDQ2861729

Jaume Llibre, Claudia Valls

Publication date: 11 November 2013

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

Full work available at URL: http://ddd.uab.cat/record/150560

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03) Symmetries, invariants, etc. in context of PDEs (35B06) Euler equations (35Q31)

Related Items

Approximate streamsurfaces for flow visualization, Analysis of stationary points and their bifurcations in the ABC-flow

Cites Work

• Unnamed Item
• The \(ABC\)-flow is not integrable for \(A=B\)
• An analytic proof of the nonintegrability of the ABC-flow for \(A=B=C\)
• Non-integrability of ABC flow
• Integrability and non-integrability in Hamiltonian mechanics
• On theC¹non-integrability of differential systems via periodic orbits
• Instability criteria for the flow of an inviscid incompressible fluid
• On the absence of a real-analytic first integral for ABC flow when A=B
• Instability criteria for steady flows of a perfect fluid
• SPLITTING OF THE SEPARATRICES AND THE NONEXISTENCE OF FIRST INTEGRALS IN SYSTEMS OF DIFFERENTIAL EQUATIONS OF HAMILTONIAN TYPE WITH TWO DEGREES OF FREEDOM
• A Geometric Approach to Regular Perturbation Theory with an Application to Hydrodynamics
• Forgotten and neglected theories of Poincaré
• Differential Galois theory and non-integrability of Hamiltonian systems