Dimensions of Fractals Generated by Bi-Lipschitz Maps
Joint Authors
Source
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
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