Multifractal spectra of in-homogenous self-similar measures

L. Olsen; N. Snigireva

doi:10.1512/iumj.2008.57.3622

Multifractal spectra of in-homogenous self-similar measures

L. Olsen, N. Snigireva

University of St Andrews

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

20 Citations (Scopus)

Abstract

Let S_i : ℝ^d → ℝ^d for i = 1,... ,N be contracting similarities. Also, let (p₁,...,P _N, p) be a probability vector and let v be a probability measure on ℝ^d with compact support. Then there exists a unique probability measure μ on ℝ^d such that (Equation Presented) The measure μ is called an in-homogenous self-similar measure.

Original language	English
Pages (from-to)	1789-1843
Number of pages	55
Journal	Indiana University Mathematics Journal
Volume	57
Issue number	4
DOIs	https://doi.org/10.1512/iumj.2008.57.3622
Publication status	Published - 2008
Externally published	Yes

Keywords

In-homogenous self-similar measure
In-homogenous self-similar set
L
Multifractal spectra
Multifractals
Self-similar measure
Spectra

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10.1512/iumj.2008.57.3622

Cite this

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abstract = "Let Si : ℝd → ℝd for i = 1,... ,N be contracting similarities. Also, let (p1,...,P N, p) be a probability vector and let v be a probability measure on ℝd with compact support. Then there exists a unique probability measure μ on ℝd such that (Equation Presented) The measure μ is called an in-homogenous self-similar measure.",

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AB - Let Si : ℝd → ℝd for i = 1,... ,N be contracting similarities. Also, let (p1,...,P N, p) be a probability vector and let v be a probability measure on ℝd with compact support. Then there exists a unique probability measure μ on ℝd such that (Equation Presented) The measure μ is called an in-homogenous self-similar measure.

KW - In-homogenous self-similar measure

KW - In-homogenous self-similar set

KW - L

KW - Multifractal spectra

KW - Multifractals

KW - Self-similar measure

KW - Spectra

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DO - 10.1512/iumj.2008.57.3622

M3 - Article

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SP - 1789

EP - 1843

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

IS - 4

ER -

Multifractal spectra of in-homogenous self-similar measures

Abstract

Keywords

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