Electron. J. Diff. Equ., Vol. 2012 (2012), No. 78, pp. 1-6.

Polynomial differential systems with explicit non-algebraic limit cycles

Rebiha Benterki, Jaume Llibre

Abstract:
Up to now all the examples of polynomial differential systems for which non-algebraic limit cycles are known explicitly have degree at most 5. Here we show that already there are polynomial differential systems of degree at least 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.

Submitted February 13, 2012. Published May 15, 2012.
Math Subject Classifications: 34C29, 34C25.
Key Words: Non-algebraic limit cycle; polynomial vector field.

Show me the PDF file (182 KB), TEX file, and other files for this article.

Rebiha Benterki
Département de Mathématiques
Centre Universitaire de Bordj Bou Arréridj
Bordj Bou Arréridj 34265, El anasser, Algeria
email: r_benterki@yahoo.fr
Jaume Llibre
Departament de Matematiques
Universitat Autònoma de Barcelona
08193 Bellaterra, Barcelona
Catalonia, Spain
email: jllibre@mat.uab.cat

Return to the EJDE web page