Assouad type dimensions and homogeneity of fractals-Reference-Cited by-同舟云学术

Assouad type dimensions and homogeneity of fractals

Published:2014-05-13 Issue:12 Volume:366 Page:6687-6733
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Fraser Jonathan

Abstract

We investigate several aspects of the Assouad dimension and the lower dimension, which together form a natural ‘dimension pair’. In particular, we compute these dimensions for certain classes of self-affine sets and quasi-self-similar sets and study their relationships with other notions of dimension, such as the Hausdorff dimension for example. We also investigate some basic properties of these dimensions including their behaviour regarding unions and products and their set theoretic complexity.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/2014-366-12/S0002-9947-2014-06202-8/S0002-9947-2014-06202-8.pdf

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