Center problem for systems with two monomial nonlinearities
type: Item
instance of: scholarly article
title: Center problem for systems with two monomial nonlinearities
zbMATH Open document ID: 1388.34024
author: Armengol Gasull
author: Jaume Giné
author: Joan Torregrosa
published in: Communications on Pure and Applied Analysis
publication date: 2016-01-29T00:00:00Z
review text: The authors study the center problem for a planar real system which is written in the complex form as \[ \dot z=i z + A z^k \bar z^\ell+B z ^m \bar z^n \] with \(k+\ell \leq m+n, \;(k,\ell)\neq (m,n), \;A, B\in \mathbb{C}\). In the equation \(z(t)\) is \(u(t)+i v(t)\), so the phase plane is the real plane \((u,v)\). In the first theorem of the paper five series of conditions are given, the fulfillment of which yields the existence of a center at the origin of the coordinates. Then, it is proved that under some restrictions the conditions of the theorem are not only sufficient, but also necessary center conditions.
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34C14
zbMATH DE Number: 6537328
zbMATH Keywords: nondegenerate center
zbMATH Keywords: Poincaré-Lyapunov constants
zbMATH Keywords: Darboux center
zbMATH Keywords: reversible center
zbMATH Keywords: holomorphic center
zbMATH Keywords: persistent center
MaRDI profile type: Publication
full work available at URL: cpaa.2016.15.577
OpenAlex ID: W2527022315
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DOI: 10.3934/CPAA.2016.15.577
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description: scientific article; zbMATH DE number 6537328