Normal forms and global phase portraits of quadratic and cubic integrable vector fields having two nonconcentric circles as invariant algebraic curves

DOI10.1080/14689367.2016.1263600zbMath1386.34057OpenAlexW2553262082MaRDI QIDQ4599275

Alisson C. Reinol, Jaume Llibre, Marcelo Messias

Publication date: 22 December 2017

Published in: Dynamical Systems (Search for Journal in Brave)

Full work available at URL: http://ddd.uab.cat/record/221033

zbMATH Keywords

limit cyclesnormal formsglobal analysisPoincaré compactificationinvariant algebraic curvesquadratic and cubic vector fields

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Bifurcations of singular points in dynamical systems (37G10) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

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