Integrability conditions of a weak saddle in a complex polynomial differential system
type: Item
instance of: scholarly article
title: Integrability conditions of a weak saddle in a complex polynomial differential system
zbMATH Open document ID: 1495.34001
author: Claudia Valls
author: Jaume Giné
published in: Journal of Dynamical and Control Systems
publication date: 2022-01-24T00:00:00Z
review text: The paper is concerned with the local analytic integrability of a complex differential system with a weak saddle \[ \dot{x}=x+y f(x), \quad \dot{y}=-y+x g(y), \] where \[ f(x)=\sum_{j=1}^{\infty} a_{j} x^{j}, \quad g(y)=\sum_{j=1}^{\infty} b_{j} y^{j} \] are analytic functions. When $a_1,b_1$ are not all zero, the integrability conditions are completely characterized. When $a_1=b_1=0$, the integrability conditions for fixed degree of $f$ and $g$ less than or equal to 6 are also given.
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 7462067
zbMATH Keywords: integrability problem
zbMATH Keywords: weak saddle
zbMATH Keywords: Liénard complex polynomial differential systems
reviewed by: Kaiyin Huang
MaRDI profile type: Publication
full work available at URL: s10883-020-09525-y
OpenAlex ID: W3097131562
cites work: On the formal integrability problem for planar differential systems
cites work: Blow-up method to compute necessary conditions of integrability for planar differential systems
cites work: Integrability of Liénard systems with a weak saddle
cites work: The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems
cites work: The nondegenerate center problem and the inverse integrating factor
cites work: Liénard Equation and Its Generalizations
cites work: Integrability conditions of a resonant saddle in generalized Liénard-like complex polynomial differential systems
cites work: On the integrability of Liénard systems with a strong saddle
cites work: Integrability conditions of a resonant saddle perturbed with homogeneous quintic nonlinearities
cites work: Integrability conditions of a resonant saddle in Liénard-like complex systems
cites work: Integrability conditions of a weak saddle in generalized Liénard-like complex polynomial differential systems
cites work: Q4514329
cites work: The Sibirsky component of the center variety of polynomial differential systems.
cites work: The Center and Cyclicity Problems
cites work: Integrability and generalized center problem of resonant singular point
DOI: 10.1007/S10883-020-09525-Y
description: scientific article; zbMATH DE number 7462067