Multifractal formalism for self-similar measures with weak separation condition
Publication in refereed journal


Times Cited
Web of Science42WOS source URL (as at 18/01/2021) Click here for the latest count
Altmetrics Information
.

Other information
AbstractFor 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.
All Author(s) ListFeng DJ, Lau KS
Journal nameJournal de Mathématiques Pures et Appliquées
Year2009
Month10
Day1
Volume Number92
Issue Number4
PublisherGAUTHIER-VILLARS/EDITIONS ELSEVIER
Pages407 - 428
ISSN0021-7824
eISSN1776-3371
LanguagesEnglish-United Kingdom
KeywordsMoran structure; Multifractal formalism; Self-similar measures; Weak separation condition
Web of Science Subject CategoriesMathematics; MATHEMATICS; Mathematics, Applied; MATHEMATICS, APPLIED

Last updated on 2021-19-01 at 01:08