Multifractal formalism for self-similar measures with weak separation condition
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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
Volume Number92
Issue Number4
Pages407 - 428
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