Genericity of dimension drop on self-affine sets

نویسندگان
چکیده

برای دانلود رایگان 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

Genericity of Dimension Drop on Self-affine Sets

We prove that generically, for a self-affine set in R, removing one of the affine maps which defines the set results in a strict reduction of the Hausdorff dimension. This gives a partial positive answer to a folklore open question.

متن کامل

Overlapping Self-affine Sets

We study families of possibly overlapping self-affine sets. Our main example is a family that can be considered the self-affine version of Bernoulli convolutions and was studied, in the non-overlapping case, by F. Przytycki and M. Urbański [23]. We extend their results to the overlapping region and also consider some extensions and generalizations.

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 Analytical Study of Self-Affine Maps

Self-affine maps were successfully used for edge detection, image segmentation, and contour extraction. They belong to the general category of patch-based methods. Particularly, each self-affine map is defined by one pair of patches in the image domain. By minimizing the difference between these patches, the optimal translation vector of the self-affine map is obtained. Almost all image process...

متن کامل

Explicit Bounds for the Hausdorff Dimension of Certain Self-Affine Sets

A lower bound of the Hausdorff dimension of certain self-affine sets is given. Moreover, this and other known bounds such as the box dimension are expressed in terms of solutions of simple equations involving the singular values of the affinities. Keyword Codes: G.2.1;G.3

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: Statistics & Probability Letters

سال: 2017

ISSN: 0167-7152

DOI: 10.1016/j.spl.2017.02.028