Quadratic vector fields in the plane have a finite number of limit cycles

DOI10.1007/BF02699193zbMath0625.58028WikidataQ100759985 ScholiaQ100759985MaRDI QIDQ579704

Rodrigo Bamón

Publication date: 1986

Published in: Publications Mathématiques (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=PMIHES_1986__64__111_0

zbMATH Keywords

limit cyclesisolated periodic orbitshyperbolic graphsquadratic vector fieldsHilbert's 16-th problem

Mathematics Subject Classification ID

Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

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Cites Work

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• Applications of centre manifold theory
• Singularities of vector fields on the plane
• A survey of quadratic systems
• 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 of the second degree
• 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
• Separatrix and Limit Cycles of Quadratic Systems and Dulac's Theorem