Singular Vectors on Fractals and Projections of Self-similar Measures
نویسندگان
چکیده
منابع مشابه
Self-similar fractals and arithmetic dynamics
The concept of self-similarity on subsets of algebraic varieties is defined by considering algebraic endomorphisms of the variety as `similarity' maps. Self-similar fractals are subsets of algebraic varieties which can be written as a finite and disjoint union of `similar' copies. Fractals provide a framework in which, one can unite some results and conjectures in Diophantine g...
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Dube proved some undecidability on self-affine fractals. In this paper, we obtain the decidability for self-similar fractal of Dube’s type. In fact, we prove that the following problems are decidable to test if the Hausdorff dimension of a given Dube’s self-similar set is equal to its similarity dimension, and to test if a given Dube’s self-similar set satisfies the strong separation condition.
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Let d ≥ 1 be an integer and E a self-similar fractal set, which is the attractor of a uniform contracting iterated function system (UIFS) on Rd. Denote by D the Hausdorff dimension, by HD(E) the Hausdorff measure and by diam(E) the diameter of E. If the UIFS is parametrised by its contracting factor c, while the set ω of fixed points of the UIFS does not depend on c, we will show the existence ...
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Self-similar fractals arise as the unique attractors of iterated function systems (IFSs) consisting of finitely many contracting similarities satisfying an open set condition. Each point x in such a fractal F arising from an IFS S is naturally regarded as the “outcome” of an infinite coding sequence T (which need not be unique) over the alphabet Σk = {0, . . . , k − 1}, where k is the number of...
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ژورنال
عنوان ژورنال: Geometric and Functional Analysis
سال: 2020
ISSN: 1016-443X,1420-8970
DOI: 10.1007/s00039-020-00531-7