The Assouad spectrum of random self-affine carpets
نویسندگان
چکیده
منابع مشابه
Assouad Dimension of Self-affine Carpets
We calculate the Assouad dimension of the self-affine carpets of Bedford and McMullen, and of Lalley and Gatzouras. We also calculate the conformal Assouad dimension of those carpets that are not self-similar.
متن کاملThe Hausdorff Dimension of the Projections of Self-affine Carpets
We study the orthogonal projections of a large class of self-affine carpets, which contains the carpets of Bedford and McMullen as special cases. Our main result is that if Λ is such a carpet, and certain natural irrationality conditions hold, then every orthogonal projection of Λ in a non-principal direction has Hausdorff dimension min(γ, 1), where γ is the Hausdorff dimension of Λ. This gener...
متن کاملGibbs measures on self-affine Sierpinski carpets and their singularity spectrum
We consider a class of Gibbs measures on self-affine Sierpinski carpets and perform the multifractal analysis of its elements. These deterministic measures are Gibbs measures associated with bundle random dynamical systems defined on probability spaces whose geometrical structure plays a central rôle. A special subclass of these measures is the class of multinomial measures on Sierpinski carpet...
متن کاملRandom subsets of self-affine fractals
We find the almost sure Hausdorff and box-counting dimensions of random subsets of self-affine fractals obtained by selecting subsets at each stage of the hierarchical construction in a statistically self-similar manner.
متن کاملOn the Assouad dimension of self-similar sets with overlaps
It is known that, unlike the Hausdorff dimension, the Assouad dimension of a self-similar set can exceed the similarity dimension if there are overlaps in the construction. Our main result is the following precise dichotomy for self-similar sets in the line: either the weak separation property is satisfied, in which case the Hausdorff and Assouad dimensions coincide; or the weak separation prop...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 2020
ISSN: 0143-3857,1469-4417
DOI: 10.1017/etds.2020.93