Resolution of the Poincaré problem and nonexistence of algebraic limit cycles in family (I) of Chinese classification
type: Item
instance of: scholarly article
title: Resolution of the Poincaré problem and nonexistence of algebraic limit cycles in family (I) of Chinese classification
zbMATH Open document ID: 1084.34038
author: Isaac A. García
author: Jordi Sorolla
author: Javier Chavarriga
published in: Chaos, Solitons and Fractals
publication date: 2005-04-18T00:00:00Z
review text: The authors investigate one of the three families of quadratic system (in Chinese classification), which can have limit cycles. The authors prove that such family cannot have algebraic limit cycles and that any irreducible invariant curve of it has the degree at most 3.
reviewed by: Alexander Grin
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 2158622
zbMATH Keywords: algebraic limit cycle
zbMATH Keywords: Poincaré problem
MaRDI profile type: Publication
full work available at URL: j.chaos.2004.06.076
OpenAlex ID: W1978556244
cites work: Necessary conditions for the existence of invariant algebraic curves for planar polynomial systems
cites work: Algebraic limit cycles of degree 4 for quadratic systems
cites work: Transcendental limit cycles via the structure of arbitrary degree invariant algebraic curves of polynomial planar vector fields
cites work: The limit cycle of the van der Pol equation is not algebraic
cites work: Q5608221
cites work: Reduction of Singularities of the Differential Equation Ady = Bdx
cites work: On the Poincaré problem
cites work: Q3715459
cites work: Algebraic invariant curves for the Liénard equation
DOI: 10.1016/J.CHAOS.2004.06.076
Recommended article: Classification of Invariant Algebraic Curves and Nonexistence of Algebraic Limit Cycles in Quadratic Systems from Family (I) of the Chinese Classification
Recommended article: On the algebraic limit cycles of Liénard systems
Recommended article: Q5164603
Recommended article: Q4989862
Recommended article: On the multiplicity of algebraic limit cycles
Recommended article: Q3517923
Recommended article: The Poincaré problem, algebraic integrability and dicritical divisors
Recommended article: Transcendental limit cycles via the structure of arbitrary degree invariant algebraic curves of polynomial planar vector fields
Recommended article: EXPLICIT NON-ALGEBRAIC LIMIT CYCLES OF A CLASS OF POLYNOMIAL SYSTEMS
Recommended article: Q5298105
description: scientific article; zbMATH DE number 2158622