کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4668088 1345496 2007 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Divergence points of self-similar measures and packing dimension
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Divergence points of self-similar measures and packing dimension
چکیده انگلیسی

Let μ be a self-similar measure in Rd. A point x∈Rd for which the limit does not exist is called a divergence point. Very recently there has been an enormous interest in investigating the fractal structure of various sets of divergence points. However, all previous work has focused exclusively on the study of the Hausdorff dimension of sets of divergence points and nothing is known about the packing dimension of sets of divergence points. In this paper we will give a systematic and detailed account of the problem of determining the packing dimensions of sets of divergence points of self-similar measures. An interesting and surprising consequence of our results is that, except for certain trivial cases, many natural sets of divergence points have distinct Hausdorff and packing dimensions.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 214, Issue 1, 10 September 2007, Pages 267-287