منابع مشابه
On univoque points for self-similar sets
Let K ⊆ R be the unique attractor of an iterated function system. We consider the case where K is an interval and study those elements of K with a unique coding. We prove under mild conditions that the set of points with a unique coding can be identified with a subshift of finite type. As a consequence of this, we can show that the set of points with a unique coding is a graph-directed selfsimi...
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We classify binary self-similar sets, which are compact sets determined by two contractions on the plane, into four classes from the viewpoint of functional equations. In this classification, we can not only show close relationships among functions with self-similarity but also give solutions to a few open problems in other field.
متن کاملA note on univoque self-Sturmian numbers
We compare two sets of (infinite) binary sequences whose suffixes satisfy extremal conditions: one occurs when studying iterations of a unimodal continuous map from the unit interval into itself, but it also characterizes univoque real numbers; the other is an equivalent definition of characteristic Sturmian sequences. As a corollary to our study we obtain that a real number β in (1, 2) is univ...
متن کاملStatistically Self - Similar Fractal Sets
In the present paper we define statistically self-similar sets, and, using a modification of method described in [2], [3], find a Hausdorff dimension of a statistically self-similar set.
متن کاملComputability of Self-Similar Sets
We investigate computability of a self-similar set on a Euclidean space. A nonempty compact subset of a Euclidean space is called a self-similar set if it equals to the union of the images of itself by some set of contractions. The main result in this paper is that if all of the contractions are computable, then the self-similar is a recursive compact set. A further result on the case that the ...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2015
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm228-3-4