Extremal polynomials (in the sense of Stahl and Totik) play an essential role in approximation theory and potential theory in the complex plane. In this talk, we will focus on dynamical properties of asymptotically extremal polynomials associated with a non-polar planar compact set E ⊂ C. In particular, if the zeros of such polynomials are uniformly bounded then their Brolin measures converge weakly to the equilibrium measure of the compact set E. Moreover, when the compact set is regular in the sense of potential theory, filled-Julia sets of such polynomials converge to the polynomial convex hull of the set E in a suitable sense. The talk is based on the joint work with M. Efe.
