Self-similar measures associated to IFS with non-uniform contraction ratios

Sze Man Ngai; Yang Wang

doi:10.4310/AJM.2005.v9.n2.a7

Self-similar measures associated to IFS with non-uniform contraction ratios

Sze Man Ngai
, Yang Wang

Mathematical Sciences

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

23 Scopus citations

Abstract

In this paper we study the absolute continuity of self-similar measures defined by iterated function systems (IFS) whose contraction ratios are not uniform. We introduce a transversality condition for a multi-parameter family of IFS and study the absolute continuity of the corresponding self-similar measures. Our study is a natural extension of the study of Bernoulli convolutions by Solomyak, Peres, et al.

Original language	English
Pages (from-to)	227-244
Number of pages	18
Journal	Asian Journal of Mathematics
Volume	9
Issue number	2
DOIs	https://doi.org/10.4310/AJM.2005.v9.n2.a7
State	Published - 2005

Scopus Subject Areas

General Mathematics
Applied Mathematics

Keywords

Absolute continuity
Iterated function system
Self-similar measure
Transversality condition

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10.4310/AJM.2005.v9.n2.a7

Cite this

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abstract = "In this paper we study the absolute continuity of self-similar measures defined by iterated function systems (IFS) whose contraction ratios are not uniform. We introduce a transversality condition for a multi-parameter family of IFS and study the absolute continuity of the corresponding self-similar measures. Our study is a natural extension of the study of Bernoulli convolutions by Solomyak, Peres, et al.",

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AB - In this paper we study the absolute continuity of self-similar measures defined by iterated function systems (IFS) whose contraction ratios are not uniform. We introduce a transversality condition for a multi-parameter family of IFS and study the absolute continuity of the corresponding self-similar measures. Our study is a natural extension of the study of Bernoulli convolutions by Solomyak, Peres, et al.

KW - Absolute continuity

KW - Iterated function system

KW - Self-similar measure

KW - Transversality condition

UR - https://www.scopus.com/pages/publications/33846099904

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DO - 10.4310/AJM.2005.v9.n2.a7

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VL - 9

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EP - 244

JO - Asian Journal of Mathematics

JF - Asian Journal of Mathematics

IS - 2

ER -

Self-similar measures associated to IFS with non-uniform contraction ratios

Abstract

Scopus Subject Areas

Keywords

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