This analysis highlights how irregular sets in free semigroup actions can hold capacity pressure, suggesting new implications for topology.
In this paper, we investigate irregular sets in free semigroup actions from the perspective of topology. More precisely, we prove that irregular set for free semigroup with the specification property carries full capacity pressure (introduced by Xiao and Ma (2023 J. Dyn. Differ. Equ. 35 199–236)) provided it is not empty. Moreover, we show the irregular set is residual if it is not empty.
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Xiao et al. (2025) studied this question.
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