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Infinite iterated function systems with overlaps

Published online by Cambridge University Press:  10 November 2014

SZE-MAN NGAI  and
JI-XI TONG
SZE-MAN NGAI
Affiliation:
College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan 410081, China Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460-8093, USA email smngai@georgiasouthern.edu
JI-XI TONG
Affiliation:
College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan 410081, China email jxtongmath@gmail.com
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Abstract

We formulate two natural but different extensions of the weak separation condition to infinite iterated function systems of conformal contractions with overlaps, and study the associated topological pressure functions. We obtain a formula for the Hausdorff dimension of the limit sets under these weak separation conditions.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 36 , Issue 3 , May 2016 , pp. 890 - 907
Copyright
© Cambridge University Press, 2014 

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