Genericity conditions for finite cyclicity of elementary graphics

DOI10.1006/jdeq.1998.3570zbMath0930.34020OpenAlexW2064727815MaRDI QIDQ1293260

Christiane Rousseau, Ana M. Guzmán-Gómez

Publication date: 31 January 2000

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

Full work available at URL: https://doi.org/10.1006/jdeq.1998.3570

zbMATH Keywords

normal formpolynomial systemshomoclinic loopsaddle-nodelimit periodic sets

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) 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 (7)

Finite cyclicity of some graphics through a nilpotent point of saddle type inside quadratic systems ⋮ Centennial History of Hilbert's 16th Problem ⋮ Finite cyclicity of elementary graphics surrounding a focus or center in quadratic systems. ⋮ PP-graphics with a nilpotent elliptic singularity in quadratic systems and Hilbert's 16th problem. ⋮ Finite cyclicity of finite codimension nondegenerate homoclinic loops with real eigenvalues in \(\mathbb{R}^3\) ⋮ Essentially asymptotically stable homoclinic networks ⋮ Finite cyclicity of graphics with a nilpotent singularity of saddle or elliptic type

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