Galoisian and qualitative approaches to linear Polyanin-Zaitsev vector fields

DOI10.1515/math-2018-0102zbMath1441.12002arXiv1807.05272OpenAlexW2963502356MaRDI QIDQ1738238

Jorge Rodriguez-Contreras, Alberto Reyes-Linero, Primitivo Belén Acosta-Humánez

Publication date: 29 March 2019

Published in: Open Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.05272

zbMATH Keywords

stabilityintegrabilitycritical pointpolynomialLiénard equationVan der Pol equationqualitativePolyanin-Zaitsev vector field

Mathematics Subject Classification ID

Qualitative theory for ordinary differential equations (34C99) Differential algebra (12H05)

Cites Work

• Darboux integrals for Schrödinger planar vector fields via Darboux transformations
• On the integrability of polynomial vector fields in the plane by means of Picard-Vessiot theory
• Galoisian approach to integrability of Schrödinger equation
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Algebraic and qualitative remarks about the family \(yy' = (\alpha x^{m+k-1} + \beta x^{m-k-1})y + \gamma x^{2m-2k-1}\)
• Integrability of planar polynomial differential systems through linear differential equations
• PASTING AND REVERSING APPROACH TO MATRIX THEORY
• The Forced van der Pol Equation I: The Slow Flow and Its Bifurcations
• Differential Galois theory and non-integrability of Hamiltonian systems
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