Rational limit cycles of Abel equations

DOI10.3934/cpaa.2021007zbMath1471.34062OpenAlexW3122719515MaRDI QIDQ2032077

Claudia Valls, Jaume Llibre

Publication date: 16 June 2021

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/cpaa.2021007

zbMATH Keywords

Abel equationsalgebraic limit cyclesrational limit cycles

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) 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 (3)

Rational Periodic Solutions on Some Generalized Abel Equations ⋮ Rational solutions of Abel differential equations ⋮ Rational solutions of Abel trigonometric polynomial differential equations

Cites Work

• Existence of non-trivial limit cycles in Abel equations with symmetries
• Limit cycles of Abel equations of the first kind
• Stability of singular limit cycles for Abel equations
• On the polynomial limit cycles of polynomial differential equations
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• Existence of closed solutions for a polynomial first order differential equation
• Iterative approximation of limit cycles for a class of Abel equations
• The number of limit cycles for generalized Abel equations with periodic coefficients of definite sign
• On the number of solutions of the equation \(\sum^n_{j=0}a_j(t)x^j,0\leq t\leq 1\), for which \(x(0)=x(1)\)
• Center conditions. III: Parametric and model center problems
• Alien limit cycles in Abel equations
• Centers and limit cycles for a family of Abel equations
• Estimate for the number of limit cycles of Abel equation via a geometric criterion on three curves
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• Limit Cycles for a Class of Abel Equations
• A Note on the Number of Limit Cycles in Certain Two-Dimensional Systems
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• LIMIT CYCLES FOR SOME ABEL EQUATIONS HAVING COEFFICIENTS WITHOUT FIXED SIGNS
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