Dimensions of Fractals Generated by Bi-Lipschitz Maps

Joint Authors

Deng, Qi-Rong
Ngai, Sze-Man

Source

Abstract and Applied Analysis

Issue

Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-12, 12 p.

Publisher

Hindawi Publishing Corporation

Publication Date

2014-07-13

Country of Publication

Egypt

No. of Pages

12

Main Subjects

Mathematics

Abstract EN

On the class of iterated function systems of bi-Lipschitz mappings that are contractions with respect to some metrics, we introduce a logarithmic distortion property, which is weaker than the well-known bounded distortion property.

By assuming this property, we prove the equality of the Hausdorff and box dimensions of the attractor.

We also obtain a formula for the dimension of the attractor in terms of certain modified topological pressure functions, without imposing any separation condition.

As an application, we prove the equality of Hausdorff and box dimensions for certain iterated function systems consisting of affine maps and nonsmooth maps.

American Psychological Association (APA)

Deng, Qi-Rong& Ngai, Sze-Man. 2014. Dimensions of Fractals Generated by Bi-Lipschitz Maps. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-12.
https://search.emarefa.net/detail/BIM-1014218

Modern Language Association (MLA)

Deng, Qi-Rong& Ngai, Sze-Man. Dimensions of Fractals Generated by Bi-Lipschitz Maps. Abstract and Applied Analysis No. 2014 (2014), pp.1-12.
https://search.emarefa.net/detail/BIM-1014218

American Medical Association (AMA)

Deng, Qi-Rong& Ngai, Sze-Man. Dimensions of Fractals Generated by Bi-Lipschitz Maps. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-12.
https://search.emarefa.net/detail/BIM-1014218

Data Type

Journal Articles

Language

English

Notes

Includes bibliographical references

Record ID

BIM-1014218