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Dimensions in infinite iterated function systems consisting of bi-Lipschitz mapping

Chih-Yung Chu Northwest A&F University Sze-Man Ngai Georgia Southern University and Hunan Normal University

Dynamical Systems mathscidoc:1809.11001

We study infinite iterated functions systems (IIFSs) consisting of bi-Lipschitz mappings instead of conformal contractions, focusing on IFSs that do not satisfy the open set condition. By assuming the logarithmic distortion property and some cardinality growth condition, we obtain a formula for the Hausdorff, box, and packing dimensions of the limit set in terms of certain topological pressure. By assuming, in addition, the weak separation condition, we show that these dimensions are equal to the growth dimension of the limit set.
Fractal, infinite iterated function system, Hausdorff dimension
[ Download ] [ 2018-09-30 06:13:53 uploaded by smngai ] [ 1373 downloads ] [ 0 comments ] 
@inproceedings{chih-yungdimensions,
  title={Dimensions in infinite iterated function systems consisting of bi-Lipschitz mapping},
  author={Chih-Yung Chu, and Sze-Man Ngai},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180930061353225950156},
}
Chih-Yung Chu, and Sze-Man Ngai. Dimensions in infinite iterated function systems consisting of bi-Lipschitz mapping. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180930061353225950156.
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