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

DOI10.1007/s12346-015-0143-2zbMath1345.34078arXiv1502.00689OpenAlexW2157139477MaRDI QIDQ290311

Chunhua Shan, Christiane Rousseau, Huai-Ping Zhu

Publication date: 1 June 2016

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.00689

zbMATH Keywords

limit cyclecyclicitynilpotent saddlefiniteness part of Hilbert's 16th problemgraphicplanar quadratic vector fieldPoincaré first return map

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) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (1)

Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems

Cites Work

• Unnamed Item
• Bifurcations of planar vector fields. Nilpotent singularities and Abelian integrals
• Genericity conditions for finite cyclicity of elementary graphics
• Hilbert's 16th problem for quadratic vector fields
• Finite cyclicity of graphics with a nilpotent singularity of saddle or elliptic type
• Finite cyclicity of some center graphics through a nilpotent point inside quadratic systems
• Elementary graphics of cyclicity 1 and 2

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