On the integrability of the $5$-dimensional Lorenz system for the gravity-wave activity

DOI10.1090/proc/13233zbMath1353.37120OpenAlexW4211059227MaRDI QIDQ5298190

Jaume Llibre, Claudia Valls

Publication date: 14 December 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: http://ddd.uab.cat/record/182504

zbMATH Keywords

Hamiltonian systemsDarboux polynomialsexponential factorspolynomial integrabilityrational integrabilityweight-homogeneous differential systems

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Nonlinear ordinary differential equations and systems (34A34) Symmetries, invariants of ordinary differential equations (34C14) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

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Cites Work

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• Elementary First Integrals of Differential Equations
• Polynomial first integrals for quasi-homogeneous polynomial differential systems
• Liouvillian integrability of polynomial differential systems
• Global integrability of cosmological scalar fields
• Liouvillian First Integrals of Differential Equations
• Invariant algebraic surfaces of the Lorenz system
• On the analytic integrability of the $5$–dimensional Lorenz system for the gravity–wave activity

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