Center problem and \(\nu \)-cyclicity of polynomial zero-Hopf singularities with non-singular rotation axis

DOI10.1016/j.jde.2021.05.054zbMath1480.34043OpenAlexW3170971961MaRDI QIDQ2048529

Isaac A. García

Publication date: 6 August 2021

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

Full work available at URL: https://doi.org/10.1016/j.jde.2021.05.054

zbMATH Keywords

periodic orbitsPoincaré mapzero-Hopf singularity\(\nu\)-cyclicity

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23)

Related Items (1)

Zero-Hopf bifurcation in the general Van der Pol-Duffing equation

Cites Work

• A method of constructing cycles without contact around a weak focus
• Bernstein inequalities and applications to analytic geometry and differential equations
• Bifurcation of planar vector fields and Hilbert's sixteenth problem
• Cyclicity of polynomial nondegenerate centers on center manifolds
• The Center and Cyclicity Problems
• Integrable zero-Hopf singularities and three-dimensional centres
• Elements of applied bifurcation theory
• Extension of Bautin theory to any dimension
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