Cyclicity of infinite contour around certain reversible quadratic center

DOI10.1006/jdeq.1998.3538zbMath0941.34020OpenAlexW2164416515MaRDI QIDQ1293940

Grzegorz Świrszcz

Publication date: 23 September 1999

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

Full work available at URL: https://doi.org/10.1006/jdeq.1998.3538

zbMATH Keywords

quadratic systemcyclicityPoincaré spherehyperbolic vertices at infinity

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 (5)

Cyclicity of period annulus for a class of quadratic reversible systems with a nonrational first integral ⋮ The cyclicity of period annuli of a class of quadratic reversible systems with two centers ⋮ Quadratic perturbations of a quadratic reversible center of genus one ⋮ On the limit cycles bifurcating from a quadratic reversible center of genus one ⋮ Simultaneous bifurcation of limit cycles and critical periods

Cites Work

• Unnamed Item
• Quadratic systems with center and their perturbations
• Hilbert's 16th problem for quadratic vector fields
• Degenerate and non-trivial hyperbolic polycycles with two vertices
• Asymptotic properties of Abelian integrals arising in quadratic systems
• Bifurcation of limit cycles from quadratic centers
• On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
• Finitely-smooth normal forms of local families of diffeomorphisms and vector fields
• Finite cyclicity of loops and cusps

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