Properties of quasi-Assouad dimension

نویسندگان

چکیده

The connections between quasi-Assouad dimension and tangents are studied. We apply these results to the calculation of for a class planar self-affine sets. also show that sets with decreasing gaps have 0 or 1 exhibit an example set in plane whose is smaller than its projection onto \(x\)-axis, showing may increase under Lipschitz mappings. Moreover, closed sets, we Hausdorff upper bound quasi-lower Assouad dimension.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Conformal Assouad Dimension and Modulus

Let α ≥ 1 and let (X, d, μ) be an α-homogeneous metric measure space with conformal Assouad dimension equal to α. Then there exists a weak tangent of (X, d, μ) with uniformly big 1-modulus.

متن کامل

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 کامل

On 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 کامل

Equi-homogeneity, Assouad Dimension and Non-autonomous Dynamics

A fractal, as originally described by Mandelbrot, is a set with an irregular and fragmented shape. Many fractals that have been extensively studied, such as self-similar sets, have the same degree of irregularity and fragmentation at all length scales. In contrast to this, an equi-homogeneous set is an irregular and fragmented shape that at each fixed scale is identical at every point. We show ...

متن کامل

6 J ul 2 00 6 ON ASYMPTOTIC ASSOUAD - NAGATA DIMENSION

For a large class of metric spaces X including discrete groups we prove that the asymptotic Assouad-Nagata dimension AN-asdim X of X coincides with the covering dimension dim(ν L X) of the Higson corona of X with respect to the sublinear coarse structure on X. Then we apply this fact to prove the equality AN-asdim(X × R) = AN-asdim X + 1. We note that the similar equality for Gromov's asymptoti...

متن کامل

ذخیره 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: Annales Fennici Mathematici

سال: 2021

ISSN: ['2737-0690', '2737-114X']

DOI: https://doi.org/10.5186/aasfm.2021.4618