Center problem and \(\nu \)-cyclicity of polynomial zero-Hopf singularities with non-singular rotation axis
type: Item
instance of: scholarly article
title: Center problem and \(\nu \)-cyclicity of polynomial zero-Hopf singularities with non-singular rotation axis
zbMATH Open document ID: 1480.34043
published in: Journal of Differential Equations
publication date: 2021-08-06T00:00:00Z
review text: The family of systems \[ \dot{x}=-y +F_1(x,y,z;\lambda), \dot{y}=x +F_2(x,y,z;\lambda), \dot{z}=F_3(x,y,z;\lambda) \] is considered, where \(F_k\) are polynomials of \((x,y,z)\) without constant or linear terms and \(\lambda\in\mathbb{R}^p\) collects the set of their coefficients. It is also assumed \(F_1=F_2=0\), \(F_3\not\equiv 0\) at \(x=y=0\). The purpose of the paper is to obtain some three-dimensional extension (near the origin) to the classical planar Poincaré-Lyapunov center problem and Bautin theory. In particular, the cubic truncated normal form of the system is considered as an example.
reviewed by: Iliya D. Iliev
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 7379529
zbMATH Keywords: zero-Hopf singularity
zbMATH Keywords: periodic orbits
zbMATH Keywords: Poincaré map
zbMATH Keywords: \(\nu\)-cyclicity
author: Isaac A. García
MaRDI profile type: Publication
full work available at URL: j.jde.2021.05.054
OpenAlex ID: W3170971961
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DOI: 10.1016/J.JDE.2021.05.054
description: scientific article; zbMATH DE number 7379529