On Dynamics of Asymptotically Minimal Polynomials

Abstract

We study dynamical properties of asymptotically extremal polynomials associated with a non-polar planar compact set E. In particular, we prove that if the zeros of such polynomials are uniformly bounded then their Brolin measures converge weakly to the equilibrium measure of E. In addition, if E is regular and the zeros of such polynomials are sufficiently close to E then we prove that the filled Julia sets converge to polynomial convex hull of E in the Klimek topology.

Minor revisions, to appear in Journal of Approximation Theory

References in corpus (3)

• Shapes of Polynomial Julia Sets
• Weak limits of the measures of maximal entropy for Orthogonal polynomials
• On Lagrange polynomials and the rate of approximation of planar sets by polynomial Julia sets

Cited by in corpus (1)

• Convergence of Equilibrium Measures under $K$-regular Polynomial Sequences and their Derivatives