{'fraction_non_alphanumeric': 0.04008438818565401, 'fraction_numerical': 0.002109704641350211, 'mean_word_length': 4.053191489361702, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Singular Perturbations of Zn with Multiple poles

We study the dynamics of the family of complex maps given by fλ(z) = zn + λ/((z - a)da(z - b)db) where n ≥ 2 is an integer and λ is an arbitrarily small complex parameter. We focus on the topological characteristics of the Julia set and the Fatou set of fλ(z). We prove that despite the large amount of possibilities there are only four different cases that correspond to different positions and orders of the poles a and b.