Polynomial differential systems with explicit non-algebraic limit cycles
Benterki, Rebiha (Centre Universitaire de Bordj Bou Arréridj. Département de Mathématiques (Algeria))
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.
Grants:	Ministerio de Ciencia y Tecnología MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Note:	Agraïments/Ajudes: The second author is partially supported by the Algerian Ministry of Higher Education and Scientific Research under project B03320090002.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
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 (research output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles