Cyclicity of degenerate polycycles through a saddle-node and two hyperbolic saddles

DOI10.1007/s10114-004-0492-2zbMath1094.34027OpenAlexW2136700298MaRDI QIDQ2581173

Lincheng Zhao

Publication date: 9 January 2006

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-004-0492-2

zbMATH Keywords

planar vector fieldcyclicitydegenerate polycyclefinitely-smooth normal formtransition maphp-connection

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Cites Work

• Unnamed Item
• Cyclicity of planar polycycles and ensembles with codimension 3 degeneration through a saddle-node and two hyperbolic saddles
• Hilbert's 16th problem for quadratic vector fields
• Bifurcations of infinite polycycles for polynomic vector fields on the plane
• 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
• Elementary graphics of cyclicity 1 and 2
• Degenerate and non-trivial hyperbolic 2-polycycles: appearance of two independent Ecalle-Roussarie compensators and Khovanskii's theory
• Hilbert's 16th problem for quadratic systems and cyclicity of elementary graphics
• Cyclicity of elementary polycycles and ensembles with codimension \(3\) degeneration.

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