Sensitive Group Actions on Regular Curves of Almost ≤ n Order
ACTA MATHEMATICA SINICA-ENGLISH SERIES(2023)
摘要
Let X be a regular curve and n be a positive integer such that for every nonempty open set U ⊂ X , there is a nonempty connected open set V ⊂ U with the cardinality ∣∂ x ( V )∣≤ n . We show that if X admits a sensitive action of a group G , then G contains a free subsemigroup and the action has positive geometric entropy. As a corollary, X admits no sensitive nilpotent group action.
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关键词
Sensitivity,regular curve,ping pong game,geometric entropy,nilpotent group
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