• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.191-199
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• 1996

The strong shift equivalence of nonnegative integral square matrices is a necessary and sufficient condition for the topological conjugacy of topological Markov chains. In this paper we study the relation between strong shift equivalence and matrix conjugation.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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• pp.87-99
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• 2017

To indicate the statistical complexity of dynamical systems, we introduce the notions of higher order irregular set and higher order maximal Birkhoff average oscillation in this paper. We prove that, in the setting of topologically mixing Markov chain, the set consisting of those points having maximal k-order Birkhoff average oscillation for all positive integers k is as large as the whole space from the topological point of view. As applications, we discuss the corresponding results on a repeller.