Abstract

Given λ∈(0,1), let Eλ be the self-similar set generated by the iterated function system (IFS) {x/3,(x+λ)/3,(x+2)/3}. Then Eλ is a self-similar set with overlaps. We obtain sufficient and necessary condition for Eλ to be totally self-similar, which is a concept first introduced by Broomhead, Montaldi, and Sidorov in 2004. When
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