The reduced Bautin index of planar vector fields

DOI10.1215/S0012-7094-99-10015-9zbMath0947.34013OpenAlexW2010608537MaRDI QIDQ1974968

Jean-Jacques Risler, Herwig Hauser, Bernard Teissier

Publication date: 27 March 2000

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-99-10015-9

zbMATH Keywords

Hilbert's 16th problemintegral closureBautin index

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Commutative Noetherian rings and modules (13E05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Dynamics induced by flows and semiflows (37C10) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (5)

Examples of center cyclicity bounds using the reduced Bautin depth ⋮ The Hopf cyclicity of the centers of a class of quintic polynomial vector fields ⋮ Continuous division of differential operators ⋮ The cyclicity of polynomial centers via the reduced Bautin depth ⋮ A Rolle type theorem for cyclicity of zeros of families of analytic functions

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• Algebraic families of analytic functions. I
• A rank theorem for analytic maps between power series spaces
• Formal cohomology. I

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