Finite cyclicity of some center graphics through a nilpotent point inside quadratic systems

DOI10.1090/MOSC/248zbMath1334.34077arXiv1506.07104OpenAlexW2964163293MaRDI QIDQ2788924

Robert Roussarie, Christiane Rousseau

Publication date: 23 February 2016

Published in: Transactions of the Moscow Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.07104

zbMATH Keywords

Hilbert's 16th problemquadratic vector fieldsfinite cyclicitycenter graphicgraphic through a nilpotent point

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (2)

Finite cyclicity of some graphics through a nilpotent point of saddle type inside quadratic systems ⋮ The number of limit cycles for regularized piecewise polynomial systems is unbounded

Cites Work

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• Bifurcations of planar vector fields. Nilpotent singularities and Abelian integrals
• Hilbert's 16th problem for quadratic vector fields
• Finite cyclicity of graphics with a nilpotent singularity of saddle or elliptic type
• Finite cyclicity of nilpotent graphics of pp-type surrounding a center
• Finitely-smooth normal forms of local families of diffeomorphisms and vector fields
• Hilbert's 16th problem for quadratic systems and cyclicity of elementary graphics
• Canard cycles and center manifolds

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