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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The dimensions of a non-conformal repeller and an average conformal repeller


Authors: Jungchao Ban, Yongluo Cao and Huyi Hu
Journal: Trans. Amer. Math. Soc. 362 (2010), 727-751
MSC (2000): Primary 37D35; Secondary 37C45
Published electronically: July 29, 2009
MathSciNet review: 2551504
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Abstract: In this paper, using thermodynamic formalism for the sub-additive potential, upper bounds for the Hausdorff dimension and the box dimension of non-conformal repellers are obtained as the sub-additive Bowen equation. The map $ f$ only needs to be $ C^1$, without additional conditions. We also prove that all the upper bounds for the Hausdorff dimension obtained in earlier papers coincide. This unifies their results. Furthermore we define an average conformal repeller and prove that the dimension of an average conformal repeller equals the unique root of the sub-additive Bowen equation.


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Additional Information

Jungchao Ban
Affiliation: Department of Applied Mathematics, National Dong Hwa University, Hualien 97401, Taiwan – and – Taida Institute for Mathematical Science, National Taiwan University, Taipei 10617, Taiwan
Email: jcban@mail.ndhu.edu.tw

Yongluo Cao
Affiliation: Department of Mathematics, Suzhou University, Suzhou, 215006, Jiangsu, People’s Republic of China – and – Institute of Mathematics, Fudan University, Shanghai, 200433, People’s Republic of China
Email: ylcao@suda.edu.cn, sudacaoyongluo@gmail.com

Huyi Hu
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email: hu@math.msu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04922-8
PII: S 0002-9947(09)04922-8
Keywords: Hausdorff dimension, non-conformal repellers, topological pressure
Received by editor(s): November 6, 2007
Published electronically: July 29, 2009
Additional Notes: Yongluo Cao is the corresponding author.
Article copyright: © Copyright 2009 American Mathematical Society