Non‐autonomous iteration of polynomials in the complex plane

Abstract We consider a sequence of polynomials with uniformly bounded zeros and , for , satisfying certain asymptotic conditions. We prove that the function sequence is uniformly convergent in . The non‐autonomous filled Julia set generated by the polynomial sequence is defined and shown to be compact and regular with respect to the Green function. Our toy example is generated by , where is the classical Chebyshev polynomial of degree .