Multifractal formalism for self-similar measures with weak separation condition
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摘要For any self-similar measure mu on R(d) satisfying the weak separation condition, we show that there exists an open ball U(0) with mu(U(0)) > 0 such that the distribution of mu, restricted on U(0), is controlled by the products of a family of non-negative matrices, and hence mu vertical bar U(0) satisfies a kind of quasi-product property. Furthermore, the multifractal formalism for mu vertical bar U(0) is valid on the whole range of dimension spectrum, regardless of whether there are phase transitions. Moreover the dimension spectra of mu and mu vertical bar U(0) coincide for q >= 0. This result unifies and improves many of the recent works on the multifractal structure of self-similar measures with overlaps. (C) 2009 Elsevier Masson SAS. All rights reserved.
著者Feng DJ, Lau KS
期刊名稱Journal de Mathématiques Pures et Appliquées
出版年份2009
月份10
日期1
卷號92
期次4
出版社GAUTHIER-VILLARS/EDITIONS ELSEVIER
頁次407 - 428
國際標準期刊號0021-7824
電子國際標準期刊號1776-3371
語言英式英語
關鍵詞Moran structure; Multifractal formalism; Self-similar measures; Weak separation condition
Web of Science 學科類別Mathematics; MATHEMATICS; Mathematics, Applied; MATHEMATICS, APPLIED

上次更新時間 2021-02-03 於 00:58