{'fraction_non_alphanumeric': 0.06287425149700598, 'fraction_numerical': 0.0, 'mean_word_length': 3.4078947368421053, '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': 1, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Thick Sets and Dynamics of Operators

Let X be a separable Banach space. For any pair U,V of nonempty open subsets in X, let NT(U,V )= {n ∈ N : T n U ∩ V � ∅}. In the present paper we show the bounded operator T on X is hereditarily hypercyclic if and only if for every pair U,V of nonempty open subsets in X, NT(U,V ) is a thick set.