Treffer: Hausdorff dimensions of the divergence points of self-similar measures with the open set condition
Title:
Hausdorff dimensions of the divergence points of self-similar measures with the open set condition
Authors:
Source:
Nonlinearity (Bristol. Print). 25(1):93-105
Publisher Information:
Bristol: Institute of Physics, 2012.
Publication Year:
2012
Physical Description:
print, 22 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Theoretical physics, Physique théorique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Topologie. Variétés et complexes cellulaires. Analyse globale et analyse sur variétés, Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds, Analyse globale, analyse sur des variétés, Global analysis, analysis on manifolds, Physique, Physics, Generalites, General, Méthodes mathématiques en physique, Mathematical methods in physics, Divers, Other topics in mathematical methods in physics, Analyse non linéaire, Nonlinear analysis, análisis no lineal, Autosimilitude, Selfsimilarity, Autosimilitud, Dimension Hausdorff, Hausdorff dimension, Dimensión Hausdorff, Divergence, Divergencia, Physique mathématique, Mathematical physics, Física matemática, Support, Soporte, Ensemble ouvert, Point accumulation
Document Type:
Fachzeitschrift
Article
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematics, South China University of Technology, Guangzhou 510641, China
Department of Mathematics, Zhangzhou Normal University, Zhangzhou 363000, China
Department of Mathematics, Zhangzhou Normal University, Zhangzhou 363000, China
ISSN:
0951-7715
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Theoretical physics
Theoretical physics
Accession Number:
edscal.25413656
Database:
PASCAL Archive
Weitere Informationen
Let μ be the self-similar measure supported on the self-similar set K with the open set condition. For x ∈ K, let A(D(x)) denote the set of accumulation points of Dr (x) := log μ (B(x,r))/log r as r ↘ 0. In this paper, we show that the set A(D(x)) is either a singleton or a closed subinterval of ℝ for any x ∈ K, and for any closed subinterval I ⊂ ℝ determines the Hausdorff dimension of the set of points x for which the set A(D(x)) equals I. Our main result solves the conjecture posed by Olsen and Winter (2003 J. Lond. Math. Soc. 67 103-22) positively and generalizes the classical result of Arbeiter and Patzschke (1996 Math. Nachr. 181 5-42).