{'fraction_non_alphanumeric': 0.0319634703196347, 'fraction_numerical': 0.0060882800608828, 'mean_word_length': 4.39344262295082, '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}}
Asymptotic Values, Prepoles, and Periodic Points

The dynamics of map Fα,β(z) = 1/(α + βe-z) are explored for portions of the real parameter plane where no fixed points are present on the real line. Careful tracking of the prepoles of order k and their relationship to asymptotic values yields regions in the parameter plane where attracting or elliptic cycles of period k + 2 are found. When α is fixed, it is shown for k = 0 that except for at most finitely many values of β, the 2-cycles found are indeed attracting. Numerical observations indicate that higher order cycles are also attracting, and the Julia set for two different such cases is depicted.