CONVERGENCE OF JULIA SETS IN THE APPROXIMATION OF λez BY λ[1+(z/d)]d

The polynomials Pd,λ(z)≔λ[1+(z/d)]dconverge uniformly on compact sets to Eλ(z)≔λez. What this convergence means for the dynamics of these functions when iterated was first studied in Devaney et al. [preprint]. Here we show the convergence of the corresponding Julia sets in the Hausdorff metric for two cases: (1) for λ such that Eλ has an attracting periodic orbit, in which case its Julia set is a Cantor set of curves, and (2) for λ such that the Julia set of Eλ is the whole plane [Formula: see text]. Finally, we give the key ideas of the algorithms designed to illustrate this convergence.