Closed Balls Included in the Inverted Multibrot and Multicorn Sets

Abstract

The aim of this article is to compute a radius of a closed ball included in the Inverted Multibrot and Multicorn sets. More exactly, for w ∈ C^∗ a complex solution of the equation z^k−1 = −1 we compute r > 0 such that B(w,r) is included in the Inverted Multibrot set N_k of the the function z^k + 1/c, c ∈ C^∗ for every k ≥ 2 and for w ∈ C^∗ a complex solution of the equation z^k+1 = −1 we compute r > 0 such that B(w,r) is included in the Inverted Multicorn set N^∗_k of the function 
z^k + 1/c , c ∈ C^∗ for every k ≥ 2.

Key words and phrases. inverted multibrot set, inverted multicorn set.

2010 Mathematics Subject Classification. 37F45