The three-dimensional center problem for the zero-Hopf singularity

DOI10.3934/dcds.2016.36.2027zbMath1366.37051OpenAlexW2525546713MaRDI QIDQ887690

Claudia Valls, Isaac A. García

Publication date: 27 October 2015

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2016.36.2027

zbMATH Keywords

Poincaré mapthree-dimensional vector fieldzero-Hopf singularitycontinua of periodic orbits

Mathematics Subject Classification ID

Bifurcations of singular points in dynamical systems (37G10) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Periodic orbits of vector fields and flows (37C27) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items

Complex dynamics in a generalized Langford system, Zero-Hopf polynomial centers of third-order differential equations, Inverse Jacobi multiplier as a link between conservative systems and Poisson structures, On the integrability problem for the Hopf-zero singularity and its relation with the inverse Jacobi multiplier, Degenerate with respect to parameters fold-Hopf bifurcations

Cites Work

• First integrals of local analytic differential systems
• Limit cycles of differential equations
• Classification of the centers, their cyclicity and isochronicity for the generalized quadratic polynomial differential systems
• Quadratic systems with center and their perturbations
• Symétrie et forme normale des centres et foyers dégénérés
• Probleme General de la Stabilite du Mouvement. (AM-17)
• Unnamed Item