Repellors and the Stability of Julia Sets
نویسنده
چکیده
In this paper we discuss the stability of Julia sets and lled{in Julia sets of functions meromorphic in the complex plane, i. e. rational or transcendental functions or polynomials. To this end, we illustrate relations to the appearence of repellors and attractors and study some chaotic features of Julia sets. The main results are: The Julia set is stable if it is a repellor and a lled{in Julia set is stable if the corresponding Julia set is a weak repellor. The proofs do not require any assumption concerning the number of singular values, actually, the functions in question might have an innnite number of singular values. In order to illustrate the usage of lled{in Julia sets applications to (relaxed) Newton's method are described. Using the stability result for lled{in Julia sets a closing lemma for polynomials and entire transcendental functions is proven.
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