2015/06/25 by Shimomura, Takashi
#54H20 #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 37B05
paper · doi:10.48550/arxiv.1506.07666
Downarowicz and Maass (2008) have shown that every Cantor minimal homeomorphism with finite topological rank K > 1 is expansive. Bezuglyi, Kwiatkowski and Medynets (2009) extended the result to non-minimal cases. On the other hand, Gambaudo and Martens (2006) had expressed all Cantor minimal continuou surjections as the inverse limit of graph coverings. In this paper, we define a topological rank for every Cantor minimal continuous surjection, and show that every Cantor minimal continuous surjection of finite topological rank has the natural extension that is expansive.