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.