Geodesic
Polynomial differential systems with explicit non-algebraic limit cycles
Electronic journal of differential equations, Tome 2012 (2012)
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.
Classification : 34C29, 34C25
Keywords: non-algebraic limit cycle, polynomial vector field 
@article{EJDE_2012__2012__a77,
     author = {Benterki,  Rebiha and Llibre,  Jaume},
     title = {Polynomial differential systems with explicit non-algebraic limit cycles},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1261.34031},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a77/}
}
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Benterki,  Rebiha; Llibre,  Jaume. Polynomial differential systems with explicit non-algebraic limit cycles. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a77/