• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.685-692
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• 1996

Subshifts of finite type can be classified by various equivalence relations. The most important equivalence relation is undoubtedly strong shift equivalence, i.e., conjugacy. In [W], R. F. Williams introduced shift equivalence which is weaker than conjugacy but still sensitive.

• Bulletin of the Korean Mathematical Society
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• v.61 no.4
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• pp.1087-1105
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• 2024

In this paper, we study a relation between the existence of invariant Gibbs measures and the balanced property of subshifts. We show that a subshift X has an invariant Gibbs measure for f ∈ C (X, ℝ) if and only if it is balanced with respect to f.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.433-447
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• 1998

We investigate coboundary conditions for two functions defined on a mixing subshift of finite type to have the same Gibbs measure. Also we find conditions for a function to be a coboundary.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.257-267
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• 1997

It is shown that if S is a positively expansive endomorphism on a one-sided mixing SFT (X,T), then (X,S) is conjugate to a one-sided mixing SFT, and the Parry measures of (X,T) and (X,S) are identical.

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.383-399
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• 2020

Following Matsumoto's definition of continuous orbit equivalence for one-sided subshifts of finite type, we introduce the notion of orbit equivalence to canonically associated dynamical systems, called the limit dynamical systems, of self-similar groups. We show that the limit dynamical systems of two self-similar groups are orbit equivalent if and only if their associated Deaconu groupoids are isomorphic as topological groupoids. We also show that the equivalence class of Cuntz-Pimsner groupoids and the stably isomorphism class of Cuntz-Pimsner algebras of self-similar groups are invariants for orbit equivalence of limit dynamical systems.

• Honam Mathematical Journal
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• v.29 no.3
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• pp.341-350
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• 2007

A dynamical system with a skew-commuting involution map is called a flip system. Every flip system on a subshift of finite type is represented by a pair of matrices, one of which is a permutation matrix. The transposition number of this permutation matrix is studied. We define an invariant, called the flip number, that measures the complexity of a flip system, and prove some results on it. More properties of flips on subshifts of finite type with symmetric adjacency matrices are investigated.