• 대한수학회보
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• 제60권2호
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• pp.349-359
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• 2023

In this paper, we study ∆-transitivity, ∆-weak mixing and ∆-mixing for semigroup actions and give several characterizations of them, which generalize related results in the literature.

• 대한수학회보
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• 제58권1호
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• pp.133-146
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• 2021

For pseudo-free and recurrent self-similar groups, we show that continuous orbit equivalence of inverse semigroup partial actions implies continuous orbit equivalence of group actions. Conversely, if group actions are continuous orbit equivalent, and the induced homeomorphism commutes with the shift maps on their groupoids, we obtain continuous orbit equivalence of inverse semigroup partial actions.

• 대한수학회보
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• 제56권6호
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• pp.1577-1588
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• 2019

We show a multiple recurrence theorem for topological dynamical systems with countable directed partial semigroup actions, which generalizes the well-know IP-version of multiple recurrence theorem proved by Furstenberg and Weiss.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권4호
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• pp.307-315
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• 2007

We study crossed products of the free group and semigroup $C^*-algebras$ by actions of ${\mathbb{R}$, i.e., flows, and estimate and compute their stable rank.

• 대한수학회지
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• 제45권1호
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• pp.221-228
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• 2008

In this paper, we study the complexity of semigroup actions using complexity functions of open covers. The main results are as follows: (1) A dynamical system is equicontinuous if and only if any open cover has bounded complexity; (2) Weak-mixing implies scattering; (3) We get a criterion for the scattering property.

• 대한수학회보
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• 제55권4호
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• pp.1125-1135
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• 2018

We show that for an M-action on a compact Hausdorff uniform space, if it has at least two disjoint compact invariant subsets, then it is thickly syndetically sensitive. Additionally, we point out that for a P-M-action of a discrete abelian group on a compact Hausdorff uniform space, the multi-sensitivity is equivalent to both thick sensitivity and thickly syndetic sensitivity.