Inhomogeneous self-similar sets and box dimensions

Jonathan M. Fraser. "Inhomogeneous self-similar sets and box dimensions." Studia Mathematica 213.2 (2012): 133-156. <http://eudml.org/doc/285576>.

@article{JonathanM2012,
abstract = {We investigate the box dimensions of inhomogeneous self-similar sets. Firstly, we extend some results of Olsen and Snigireva by computing the upper box dimensions assuming some mild separation conditions. Secondly, we investigate the more difficult problem of computing the lower box dimension. We give some non-trivial bounds and provide examples to show that lower box dimension behaves much more strangely than upper box dimension, Hausdorff dimension and packing dimension.},
author = {Jonathan M. Fraser},
journal = {Studia Mathematica},
keywords = {inhomogeneous self-similar set; box dimension; covering regularity exponent},
language = {eng},
number = {2},
pages = {133-156},
title = {Inhomogeneous self-similar sets and box dimensions},
url = {http://eudml.org/doc/285576},
volume = {213},
year = {2012},
}

TY - JOUR
AU - Jonathan M. Fraser
TI - Inhomogeneous self-similar sets and box dimensions
JO - Studia Mathematica
PY - 2012
VL - 213
IS - 2
SP - 133
EP - 156
AB - We investigate the box dimensions of inhomogeneous self-similar sets. Firstly, we extend some results of Olsen and Snigireva by computing the upper box dimensions assuming some mild separation conditions. Secondly, we investigate the more difficult problem of computing the lower box dimension. We give some non-trivial bounds and provide examples to show that lower box dimension behaves much more strangely than upper box dimension, Hausdorff dimension and packing dimension.
LA - eng
KW - inhomogeneous self-similar set; box dimension; covering regularity exponent
UR - http://eudml.org/doc/285576
ER -