Some families of quadratic systems with at most one limit cycle

DOI10.56415/basm.y2023.i1.p8MaRDI QIDQ6066920

Jaume Llibre

Publication date: 16 November 2023

Published in: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica (Search for Journal in Brave)

zbMATH Keywords

limit cyclesquadratic systems16th Hilbert problem

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)

Cites Work

• Quadratic vector fields in the plane have a finite number of limit cycles
• A survey of quadratic systems
• Algebraic Particular Integrals, Integrability and the Problem of the Center
• On the number of limit cycles of the equation \frac{𝑑𝑦}𝑑𝑥=\frac{𝑃(𝑥,𝑦)}𝑄(𝑥,𝑦), where 𝑃 and 𝑄 are polynomials
• Limit Cycles for a Class of Abel Equations
• Separatrix and Limit Cycles of Quadratic Systems and Dulac's Theorem
• On General Properties of Quadratic Systems
• Mathematical problems
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