Conformal Iterated Function Systems with Overlaps

Qi Rong Deng; Sze Man Ngai

doi:10.1080/14689367.2010.497478

Conformal Iterated Function Systems with Overlaps

Qi Rong Deng, Sze Man Ngai

Mathematical Sciences

Fujian Normal University

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

13 Scopus citations

Abstract

For a conformal iterated function system satisfying the bounded distortion property and the weak separation condition, we prove a formula for the Hausdorff dimension of the attractor, and establish the equality between the Hausdorff dimension and the growth dimension. Furthermore, a relation between the open set condition and the weak separation condition is given.

Original language	American English
Journal	Dynamical Systems: An International Journal
Volume	26
DOIs	https://doi.org/10.1080/14689367.2010.497478
State	Published - Jan 1 2011

Disciplines

Education
Mathematics

Keywords

Bounded distortion property
Conformal iterated function system
Growth dimension
Hausdorff dimension
Topological pressure
Weak separation condition

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https://doi.org/10.1080/14689367.2010.497478

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title = "Conformal Iterated Function Systems with Overlaps",

abstract = "For a conformal iterated function system satisfying the bounded distortion property and the weak separation condition, we prove a formula for the Hausdorff dimension of the attractor, and establish the equality between the Hausdorff dimension and the growth dimension. Furthermore, a relation between the open set condition and the weak separation condition is given.",

keywords = "Bounded distortion property, Conformal iterated function system, Growth dimension, Hausdorff dimension, Topological pressure, Weak separation condition",

author = "Deng, {Qi Rong} and Ngai, {Sze Man}",

year = "2011",

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day = "1",

doi = "10.1080/14689367.2010.497478",

language = "American English",

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journal = "Dynamical Systems: An International Journal",

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TY - JOUR

T1 - Conformal Iterated Function Systems with Overlaps

AU - Deng, Qi Rong

AU - Ngai, Sze Man

PY - 2011/1/1

Y1 - 2011/1/1

N2 - For a conformal iterated function system satisfying the bounded distortion property and the weak separation condition, we prove a formula for the Hausdorff dimension of the attractor, and establish the equality between the Hausdorff dimension and the growth dimension. Furthermore, a relation between the open set condition and the weak separation condition is given.

AB - For a conformal iterated function system satisfying the bounded distortion property and the weak separation condition, we prove a formula for the Hausdorff dimension of the attractor, and establish the equality between the Hausdorff dimension and the growth dimension. Furthermore, a relation between the open set condition and the weak separation condition is given.

KW - Bounded distortion property

KW - Conformal iterated function system

KW - Growth dimension

KW - Hausdorff dimension

KW - Topological pressure

KW - Weak separation condition

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/125

UR - https://doi.org/10.1080/14689367.2010.497478

U2 - 10.1080/14689367.2010.497478

DO - 10.1080/14689367.2010.497478

M3 - Article

VL - 26

JO - Dynamical Systems: An International Journal

JF - Dynamical Systems: An International Journal

ER -

Conformal Iterated Function Systems with Overlaps

Abstract

Disciplines

Keywords

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