11 citations · 15 across the 13 of their papers we have counts for
6 papers · 1 filter
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…