Polynomials without repelling periodic point of given period

Bergweiler proved that for any given integer k 2, every polynomial P of degree d 2 has at least one repelling periodic cycle of period k unless (k, d) ∈ {(2, 2), (2, 3), (2, 4), (3, 2)}. Here we classified these exceptional polynomials. We also showed that the Julia sets of these exceptional polynomials are connected. © 2005 Elsevier Inc. All rights reserved.