Multifractal Formalism for Self-Affine Measures with Overlaps

Qi Rong Deng; Sze Man Ngai

doi:10.1007/s00013-009-2969-9

Multifractal Formalism for Self-Affine Measures with Overlaps

Qi Rong Deng
, Sze Man Ngai

Mathematical Sciences

Fujian Normal University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We prove that for a class of self-affine measures defined by an expanding matrix whose eigenvalues have the same modulus, the L ^q -spectrum τ(q) is differentiable for all q > 0. Furthermore, we prove that the multifractal formalism holds in the region corresponding to q > 0.

Original language	American English
Journal	Archiv der Mathematik
Volume	92
DOIs	https://doi.org/10.1007/s00013-009-2969-9
State	Published - Jun 1 2009

Disciplines

Education
Mathematics

Keywords

Asymptotic weak separation condition
Dimension spectrum
Iterated function system with overlaps
L q –spectrum
Multifractal formalism
Primary 28A80
Secondary 28A78
Self-affine measure

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https://doi.org/10.1007/s00013-009-2969-9

Cite this

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title = "Multifractal Formalism for Self-Affine Measures with Overlaps",

abstract = "We prove that for a class of self-affine measures defined by an expanding matrix whose eigenvalues have the same modulus, the L q -spectrum τ(q) is differentiable for all q > 0. Furthermore, we prove that the multifractal formalism holds in the region corresponding to q > 0.",

keywords = "Asymptotic weak separation condition, Dimension spectrum, Iterated function system with overlaps, L q –spectrum, Multifractal formalism, Primary 28A80, Secondary 28A78, Self-affine measure",

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AU - Deng, Qi Rong

AU - Ngai, Sze Man

PY - 2009/6/1

Y1 - 2009/6/1

N2 - We prove that for a class of self-affine measures defined by an expanding matrix whose eigenvalues have the same modulus, the L q -spectrum τ(q) is differentiable for all q > 0. Furthermore, we prove that the multifractal formalism holds in the region corresponding to q > 0.

AB - We prove that for a class of self-affine measures defined by an expanding matrix whose eigenvalues have the same modulus, the L q -spectrum τ(q) is differentiable for all q > 0. Furthermore, we prove that the multifractal formalism holds in the region corresponding to q > 0.

KW - Asymptotic weak separation condition

KW - Dimension spectrum

KW - Iterated function system with overlaps

KW - L q –spectrum

KW - Multifractal formalism

KW - Primary 28A80

KW - Secondary 28A78

KW - Self-affine measure

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/122

UR - https://doi.org/10.1007/s00013-009-2969-9

U2 - 10.1007/s00013-009-2969-9

DO - 10.1007/s00013-009-2969-9

M3 - Article

SN - 0003-889X

VL - 92

JO - Archiv der Mathematik

JF - Archiv der Mathematik

ER -

Multifractal Formalism for Self-Affine Measures with Overlaps

Abstract

Disciplines

Keywords

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