![]() Parameters 1/2<1, and similarly for Sinai's problem on iterated function systemsĪ central ingredient of the proof is an inverse theorem for the growth of Thus, for example, there is at most a zero-dimensional set of Non-degeneracy condition, the set of "exceptional" parameters has HausdorffÄimension 0. Parametrized in a real-analytic manner, then, under an extremely mild Of the "1-dimensional Sierpinski gasket" in irrational directions are all ofĪs another consequence, if a family of self-similar sets or measures is It also gives anĪffirmative answer to a conjecture of Furstenberg, showing that the projections ![]() This is a step towards the folklore conjecture that such a drop inÄimension is explained only by exact overlaps, and confirms the conjecture inĬases where the contraction parameters are algebraic. Similarity dimension, then at small scales there are super-exponentially closeĬylinders. We show that if the dimension is smaller than the minimum of 1 and the We study the Hausdorff dimension of self-similar sets and measures on the The third application partially answers a problem posed by Barrera. Thirdly, for the doubling map with asymmetrical holes, we give a sufficient condition such that the attractor can be identified with a subshift of finite type. This application generalizes a result of de Vries and Komornik. Secondly, in the setting of β-expansions, when the set of all the unique codings is not a subshift of finite type, we can calculate in some cases the Hausdorff dimension of the univoque set. Firstly, we calculate the Hausdorff dimension of the set of points of K with multiple codings. We give three different applications of our main result. With this identification, we can calculate the Hausdorff dimension of K as well as the set of elements in K with unique codings using the machinery of Mauldin and Williams. In this paper we prove, under some assumptions, that K can be identified with a subshift of finite type. Let K â R be a self-similar set generated by some iterated function system.
0 Comments
Leave a Reply. |