11 citations · 12 across the 5 of their papers we have counts for
5 papers
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…
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…