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

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.

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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

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