Multifractal measures and a weak separation condition

Ka Sing Lau; Sze Man Ngai

doi:10.1006/aima.1998.1773

Multifractal measures and a weak separation condition

Ka Sing Lau
, Sze Man Ngai

Mathematical Sciences

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

183 Scopus citations

Abstract

We define a new separation property on the family of contractive similitudes that allows certain overlappings. This property is weaker than the open set condition of Hutchinson. It includes the well-known class of infinite Bernoulli convolutions associated with the P.V. numbers and the solutions of the two-scale dilation equations. Our main purpose in this paper is to prove the multifractal formalism under such condition.

Original language	English
Pages (from-to)	45-96
Number of pages	52
Journal	Advances in Mathematics
Volume	141
Issue number	1
DOIs	https://doi.org/10.1006/aima.1998.1773
State	Published - Jan 15 1999

Scopus Subject Areas

General Mathematics

Keywords

Dimension spectrum
Multifractal measure
Self-similarity
Stopping time
Strict convexity
Thermodynamic formalism

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10.1006/aima.1998.1773

Cite this

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AB - We define a new separation property on the family of contractive similitudes that allows certain overlappings. This property is weaker than the open set condition of Hutchinson. It includes the well-known class of infinite Bernoulli convolutions associated with the P.V. numbers and the solutions of the two-scale dilation equations. Our main purpose in this paper is to prove the multifractal formalism under such condition.

KW - Dimension spectrum

KW - Multifractal measure

KW - Self-similarity

KW - Stopping time

KW - Strict convexity

KW - Thermodynamic formalism

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DO - 10.1006/aima.1998.1773

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VL - 141

SP - 45

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JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 1

ER -

Multifractal measures and a weak separation condition

Abstract

Scopus Subject Areas

Keywords

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