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This article describes the work of Ki Hang Kim and Fred Roush on questions of decidability in algebra and number theory.
In this article we study how a subshift can simulate another one, where the notion of simulation is given by operations on subshifts inspired by the dynamical systems theory (factor, projective subaction …). There exists a correspondence between the notion of simulation and the set of forbidden...
In the early 1990’s, Kim and Roush developed path methods for establishing strong shift equivalence (SSE) of positive matrices over a dense subring
of ℝ. This paper gives a detailed, unified and generalized presentation of these path methods. New arguments which address arbitrary...
We prove that every topological dynamical system (X,T) has a zero-dimensional principal extension, i.e. a zero-dimensional extension (Y,S) such that for every S-invariant measure ν on Y the conditional entropy h(ν|X) is zero. This reduces the discussion of many entropy-related properties to the...
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