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.
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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 |
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Jaume Llibre Departament de Matematiques Universitat Autònoma de Barcelona 08193 Bellaterra, Barcelona Catalonia, Spain email: jllibre@mat.uab.cat |
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