A class of differential systems of degree even with exact non-algebraic limit cycles

Abdelkrim Kina; Aziza Berbache; Ahmed Bendjeddou

doi:10.24193/subbmath.2020.3.08

A class of differential systems of degree even with exact non-algebraic limit cycles

Authors

Abdelkrim Kina
Aziza Berbache
Ahmed Bendjeddou

DOI:

https://doi.org/10.24193/subbmath.2020.3.08

Keywords:

Planar polynomial differential system, first integral, non-algebraic limit cycle.

Abstract

Up until now all the polynomial differential systems for which
non-algebraic limit cycles are known explicitly have degree odd. Here we
show that already that there are polynomial systems of degree even has
an explicit limit cycle which is not algebraic. To our knowledge, there
are no such type of examples in the literature.