Chebyshev's method applied to polynomials with two distinct roots

Abstract

The Julia set of the Chebyshev's method applied to polynomials with exactly two distinct roots is shown to be connected, and its Fatou set is proved to be the union of attracting basins corresponding to the two roots. Further, if the two roots have the same multiplicity then the common boundary of the two immediate basins is proved to be a connected subset of the Julia set.