کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4620468 1339463 2009 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Dimension of homogeneous rational self-similar measures with overlaps
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Dimension of homogeneous rational self-similar measures with overlaps
چکیده انگلیسی

We develop a tool to analyse some self-similar measures with overlaps, those obtained from systems of homotheties with centres in a lattice where the contraction ratios are all equal to the inverse of a natural number L. We obtain the local dimension of the measure as the Shannon entropy of an associated hidden Markov chain divided by the logarithm of L. This result turns out to be useful in the study of the absolute continuity or singularity of the measure, and provides two sequences converging to the dimension of the measure, one of them non-increasing and the other non-decreasing, which allows us to obtain estimates of the dimension.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 353, Issue 1, 1 May 2009, Pages 350-361