Darboux systems with a cusp point and pseudo-abelian integrals

DOI10.1016/j.jde.2019.08.038zbMath1440.34034OpenAlexW2907818003MaRDI QIDQ2333391

Aymen Braghtha

Publication date: 13 November 2019

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2019.08.038

zbMATH Keywords

limit cyclesDarboux integrabilityfirst integralsblowing-uppseudo-abelian integrals

Mathematics Subject Classification ID

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)

Related Items (1)

A LINEAR ESTIMATION TO THE NUMBER OF ZEROS FOR ABELIAN INTEGRALS IN A KIND OF QUADRATIC REVERSIBLE CENTERS OF GENUS ONE

Cites Work

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• On the number of zeros of Abelian integrals. A constructive solution of the infinitesimal Hilbert sixteenth problem
• On limit cycles appearing by polynomial perturbation of Darbouxian integrable systems
• Pseudo-abelian integrals: unfolding generic exponential case
• Real analytic varieties with the finiteness property and complex abelian integrals
• Pseudo-Abelian integrals along Darboux cycles: A codimension one case
• Pseudo-abelian integrals on slow-fast Darboux systems
• Projections of semi-analytic sets
• Pseudo-Abelian integrals along Darboux cycles
• A method of desingularization for analytic two-dimensional vector field families

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