Abstract
Let [Formula: see text] be a self-similar set in [Formula: see text]. Generally, if the iterated function system (IFS) of [Formula: see text] has some overlaps, then some points in [Formula: see text] may have multiple codings. If an [Formula: see text] has a unique coding, then we call [Formula: see text] a univoque point. We denote by [Formula: see text] (univoque set) the set of points in [Formula: see text] having unique codings. In this paper, we shall consider the following natural question: if two self-similar sets are bi-Lipschitz equivalent, then are their associated univoque sets also bi-Lipschitz equivalent. We give a class of self-similar sets with overlaps, and answer the above question affirmatively.
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