11 citations · 15 across the 13 of their papers we have counts for
13 papers
On some properties of basic sets
Takashi Shimomura
In the theory of zero-dimensional systems and their relation to -algebras, Poon (1990) introduced a class of closed sets. We call the closed sets quasi-sections. Medynets (200…
Refinement of Bratteli-Vershik models
Takashi Shimomura
In the zero-dimensional systems, the Bratteli-Vershik models can be built upon certain closed sets that are called `quasi-sections' in this article. There exists a bijective corres…
A simple approach to substitution minimal subshifts
Takashi Shimomura
In the study of substitution minimal subshifts, some complicated trivialities have hindered simple and general approaches. Recently, Maloney and Rust introduced the term "tame," si…
Topological rank does not increase by natural extension of Cantor minimals
Takashi Shimomura
Downarowicz and Maass (2008) have defined the topological rank for all Cantor minimal homeomorphisms. On the other hand, Gambaudo and Martens (2006) have expressed all Cantor minim…
Finite rank Bratteli--Vershik homeomorphisms are expansive
Takashi Shimomura
Downarowicz and Maass (2008) have shown that every Cantor minimal homeomorphism with finite topological rank is expansive. Bezuglyi, Kwiatkowski, and Medynets (2009) extend…
Bratteli--Vershik models and graph covering models
Takashi Shimomura
Based on our previous graph covering method, we introduce weighted graph covering models and flexible graph covering models that are almost equivalent to the well-known Bratteli--V…
Proximal Cantor systems with topological rank 2 are residually scrambled
Takashi Shimomura
Downarowicz and Maass (2008) proposed topological ranks for all homeomorphic Cantor minimal dynamical systems using properly ordered Bratteli diagrams. In this study, we adopt this…
The construction of a completely scrambled system by graph covers
Takashi Shimomura
In this paper, we define a new construction of completely scrambled 0-dimensional systems using the inverse limit of sequences of directed graph covers. These examples are transiti…
Combinatorial embedding of chain transitive zero-dimensional systems into chaos
Takashi Shimomura
We show that a zero-dimensional chain transitive dynamical system can be embedded into a densely uniformly chaotic system, with dense uniformly chaotic set . We concretely const…
Non-homeomorphic topological rank and expansiveness
Takashi Shimomura
Downarowicz and Maass (2008) have shown that every Cantor minimal homeomorphism with finite topological rank is expansive. Bezuglyi, Kwiatkowski and Medynets (2009) extende…
Aperiodic homeomorphisms approximate chain mixing endomorphisms on the Cantor set
Takashi Shimomura
Let be a chain mixing continuous onto mapping from the Cantor set onto itself.Let be an aperiodic homeomorphism on the Cantor set. We show that homeomorphisms that are topo…
Graph covers and ergodicity for 0-dimensional systems
Takashi Shimomura
Bratteli--Vershik systems have been widely studied. In the context of general 0-dimensional systems, Bratteli--Vershik systems are homeomorphisms that have Kakutani--Rohlin refinem…
Chain mixing endomorphisms are approximated by subshifts on the Cantor set
Takashi Shimomura
Let f be a chain mixing continuous onto mapping from the Cantor set onto itself. Let g be a homeomorphism on the Cantor set that is topologically conjugate to a subshift. Then, hom…