STABLY INTERESTING JULIA SETS OF POLYNOMIALS

Newhouse [1] introduced the concept of thickness and used it to prove that Cantor sets in the line must intersect under certain conditions. The usual definitions of thickness do not generalize to higher dimensions, but in this Note we produce two polynomials such that any holomorphic functions which are sufficiently small C-2 perturbations of these polynomials have Julia sets which contain intersecting Canter sets. Moreover, one of the polynomials is of the form z(2)+c with \c\ large.