Electron. J. Diff. Equ.,
Vol. 2012 (2012), No. 78, pp. 16.
Polynomial differential systems with explicit nonalgebraic
limit cycles
Rebiha Benterki, Jaume Llibre
Abstract:
Up to now all the examples of polynomial differential systems for
which nonalgebraic 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
nonalgebraic 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 nonalgebraic limit cycles.
Submitted February 13, 2012. Published May 15, 2012.
Math Subject Classifications: 34C29, 34C25.
Key Words: Nonalgebraic 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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