{'fraction_non_alphanumeric': 0.017994858611825194, 'fraction_numerical': 0.0, 'mean_word_length': 4.571428571428571, '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}}
Topological Transitivity and Chaos of Group Actions on dendrites

We show that each weakly mixing group action on a dendrite must have a ping-pong game, and has positive geometric entropy when the acting group is finitely generated. As a corollary, we prove that no nilpotent group action on a dendrite is weakly mixing. At last, we show that each dendrite admits no chaotic group actions.