Note on the Equilibrium Measures of Julia sets of Exceptional Jacobi Polynomials

TL;DR

This paper demonstrates that the equilibrium measures of Julia sets associated with exceptional Jacobi polynomials converge to the equilibrium measure of their orthogonality interval, extending known results to this special class.

Contribution

It establishes the weak-star convergence of equilibrium measures for Julia sets of exceptional Jacobi polynomials, generalizing classical results to these polynomials.

Findings

Equilibrium measures of Julia sets tend to the measure of the orthogonality interval.

The convergence is in the weak-star sense.

Results extend classical Julia set measure properties to exceptional Jacobi polynomials.

Abstract

We prove that similarly to the standard case, the equilibrium measure of Julia sets of exceptional Jacobi polynomials tends to the equilibrium measure of the interval of orthogonality in weak-star sense.