Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 78, pp. 1-6.

Title:  Polynomial differential systems with explicit non-algebraic 
        limit cycles

Authors: Rebiha Benterki (Univ. de Bordj Bou Arreridj, Algeria)
         Jaume Llibre (Univ. Autonoma de Barcelona, Spain)

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.