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1.
11 p, 796.2 KB Algebraic limit cycles bifurcating from algebraic ovals of quadratic centers / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Tian, Yun (Shanghai Normal University. Department of Mathematics)
In the integrability of polynomial differential systems it is well known that the invariant algebraic curves play a relevant role. Here we will see that they can also play an important role with respect to limit cycles. [...]
2018 - 10.1142/S0218127418501456
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 28, Issue 11 (December 2018) , art. 1850145  
2.
14 p, 492.6 KB On the limit cycles bifurcating from an ellipse of a quadratic center / Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Schlomiuk, Dana (Université de Montréal(Canada). Département de Mathématiques et Statistique)
Consider the class of all quadratic centers whose period annulus has a periodic solution whose phase curve is an ellipse E. The period annulus of any of such quadratic centers has cyclicity at least one, and this one is due to a family of algebraic limit cycles(formed by ellipses) bifurcating from the ellipse E. [...]
2015 - 10.3934/dcds.2015.35.1091
Discrete and continuous dynamical systems. Series A, Vol. 35 Núm. 3 (2015) , p. 1091-1102  

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