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math.DS2020
On a kind of self-similar sets with complete overlaps
Derong Kong, Yuanyuan Yao
Let be the self-similar set generated by the {\it iterated function system} {\[ f_0(x)=\frac{x}β,\quad f_1(x)=\frac{x+1}β, \quad f_{β+1}=\frac{x+β+1}β \]}with . {Then}…
math.DS2009
Difference between Devaney chaos associated with two systems
Bingzhe Hou, Xianfeng Ma, Gongfu Liao
We discuss the relation between Devaney chaos in the base system and Devaney chaos in its induced hyperspace system. We show that the latter need not imply the former. We also argu…