2,473 research outputs found
On the points without universal expansions
Let . Given any , a sequence
is called a -expansion of if
For any and any , if there exists some such that
, then we call a
universal -expansion of .
Sidorov \cite{Sidorov2003}, Dajani and de Vries \cite{DajaniDeVrie} proved
that given any , then Lebesgue almost every point has uncountably
many universal expansions. In this paper we consider the set of
points without universal expansions. For any , let be the
-bonacci number satisfying the following equation:
Then we have
, where denotes the Hausdorff dimension.
Similar results are still available for some other algebraic numbers. As a
corollary, we give some results of the Hausdorff dimension of the survivor set
generated by some open dynamical systems. This note is another application of
our paper \cite{KarmaKan}.Comment: 15page
Lipschitz equivalence of a class of self-similar sets
We consider a class of homogeneous self-similar sets with complete overlaps
and give a sufficient condition for the Lipschitz equivalence between members
in this class.Comment: A remark was added. To appear in Ann. Acad. Sci. Fenn. Mat
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