Polynomial differential systems with explicit non-algebraic limit cycles

Agraïments/Ajudes: The second author is partially supported by the Algerian Ministry of Higher Education and Scientific Research under project B03320090002.Up to know all the examples of polynomial differential systems for which non-algebraic limit cycles are known explicitly have degree ≥ 5. Here we show that already there are polynomial differential systems of degree ≥ 3 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