Weak and strong composition conditions for the Abel differential equation

DOI10.1016/j.bulsci.2014.06.001zbMath1315.34040arXiv1306.0107OpenAlexW2964203610WikidataQ115359962 ScholiaQ115359962MaRDI QIDQ472546

Fedor Pakovitch

Publication date: 19 November 2014

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.0107

zbMATH Keywords

periodic orbitscentersAbel equationcomposition condition

Mathematics Subject Classification ID

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)

Related Items (10)

Kink solitary solutions to generalized Riccati equations with polynomial coefficients ⋮ Shuffle and Faà di Bruno Hopf algebras in the center problem for ordinary differential equations ⋮ Centers and limit cycles for a family of Abel equations ⋮ Periodic solutions of Abel equations with jumps ⋮ Parametric center-focus problem for Abel equation ⋮ Anti-periodic solutions of Abel differential equations with state dependent discontinuities ⋮ Uniform upper bounds for the cyclicity of the zero solution of the Abel differential equation ⋮ On decompositions of trigonometric polynomials ⋮ Uniformly isochronous quartic systems ⋮ Quasi-Lie families, schemes, invariants and their applications to Abel equations

Cites Work

• Unnamed Item
• On decompositions of trigonometric polynomials
• Some algebraic aspects of the center problem for ordinary differential equations
• A simple solution of some composition conjectures for Abel equations
• Parametric centers for trigonometric Abel equations
• Center conditions at infinity for Abel differential equations
• The composition conjecture for Abel equation
• Centers for trigonometric Abel equations
• Algebraic geometry of the center-focus problem for Abel differential equations
• Non-autonomous equations related to polynomial two-dimensional systems
• On a condition for a centre of cubic non-autonomous equations
• Universal centres and composition conditions
• On the trigonometric moment problem

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