Polynomial differential systems with explicit non-algebraic limit cycles
Benterki, Rebiha (Centre Universitaire de Bordj Bou Arréridj(Algeria). Département de Mathématiques)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date: 2012
Abstract: Up to know all the examples of polynomial differential systems for which non-algebraic limit cycles are known explicitly have degree ≥ 5. Here we show that already there are polynomial differential systems of degree ≥ 3 exhibiting explicit non-algebraic limit cycles. It is well known that polynomial differential systems of degree 1 (i. e. linear differential systems) has no limit cycles. It remains the open question to determine if the polynomial differential systems of degree 2 can exhibit explicit non-algebraic limit cycles.
Note: Agraïments/Ajudes: The second author is partially supported by the Algerian Ministry of Higher Education and Scientific Research under project B03320090002.
Note: Número d'acord de subvenció MCYT/MTM2008-03437
Note: Número d'acord de subvenció AGAUR/2009/SGR-410
Rights: Tots els drets reservats.
Language: Anglès
Document: article ; recerca ; acceptedVersion
Subject: Non-algebraic limit cycle ; Polynomial vector field
Published in: Electronic journal of differential equations, Vol. 2012 Núm. 78 (2012) , p. 1-6, ISSN 1072-6691



Postprint
5 p, 282.3 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 2016-05-06, last modified 2020-08-16



   Favorit i Compartir