Small amplitude periodic orbits in three-dimensional quadratic vector fields with a zero-Hopf singularity

DOI10.1007/S10884-022-10208-4MaRDI QIDQ6567196

Isaac A. García

Publication date: 4 July 2024

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

zbMATH Keywords

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

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Invariant manifolds for ordinary differential equations (34C45)

Cites Work

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• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• A method of constructing cycles without contact around a weak focus
• Bifurcation of planar vector fields and Hilbert's sixteenth problem
• Cyclicity of polynomial nondegenerate centers on center manifolds
• Center problem and \(\nu \)-cyclicity of polynomial zero-Hopf singularities with non-singular rotation axis
• The Center and Cyclicity Problems
• Integrable zero-Hopf singularities and three-dimensional centres
• Elements of applied bifurcation theory

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