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Algebraic limit cycles on quadratic polynomial differential systems
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia (Universidade de Lisboa. Departamento de Matemàtica)

Date: 2018
Abstract: Algebraic limit cycles in quadratic polynomial differential systems started to be studied in 1958, and few years later the following conjecture appeared: Quadratic polynomial differential systems have at most one algebraic limit cycle. We prove that for a quadratic polynomial differential system having an invariant algebraic curve with at most one pair of diametrally opposite singular point at infinity, has at most one algebraic limit cycle. Our result provides a partial positive answer to this conjecture.
Note: Número d'acord de subvenció EC/318999
Note: Número d'acord de subvenció EC/316338
Note: Número d'acord de subvenció MINECO/MTM2013-40998-P
Note: Número d'acord de subvenció AGAUR/2014/SGR-568
Rights: Tots els drets reservats.
Language: Anglès.
Document: article ; recerca ; submittedVersion
Subject: Algebraic limit cycles ; Quadratic polynomial differential system ; Quadratic polynomial vector field
Published in: Proceedings of the Edinburgh Mathematical Society, Vol. 61, issue 2 (May 2018) , p. 499-512, ISSN 0013-0915

DOI: 10.1017/S0013091517000244


Preprint
13 p, 721.0 KB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (scientific output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles

 Record created 2018-11-12, last modified 2019-02-02



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