{'fraction_non_alphanumeric': 0.047979797979797977, 'fraction_numerical': 0.005050505050505051, 'mean_word_length': 4.293333333333333, '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}}
Recurrence in Systems with Random perturbations

We introduce the notion of (f, δ)-recurrence for the so-called (f, δ)-processes. We show that if a function of type 2∞ has no attractive periodic points of periods greater than 2N for some positive integer N and has an infinite ω-limit set, then each point belonging to its infinite ω-limit set is (f, δ)-recurrent provided that δ is small enough.