Results and open problems on the algebraic limit cycles of the planar polynomial differential systems
Abstract: In this talk we summarize some results and open problems on the algebraic limit cycles of the planar polynomial differential systems. More precisely, (i) we study the maximum number of algebraic limit cycles of the polynomial differential differential systems of degree $n$; (ii) we show how to use the algebraic limit cycles for proving that any finite configuration of limit cycles can be realized by some polynomial differential system; (iii) we provide the maximum number of algebraic limit cycles formed by circles that a polynomial differential system of degree $n$ can exhibit; (iv) we study the algebraic limit cycles of the polynomial differential systems of degree 2.