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Title: The dimensions of a non-conformal repeller and an average conformal repeller
Authors: 班榮超
Ban, Jung-Chao
Cao, Yong-Luo
Hu, Hu-Yi
Contributors: 應數系
Date: 2010-01
Issue Date: 2020-06-22 13:44:32 (UTC+8)
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.
Relation: Transactions of the American Mathematical Society, Vol.362, No.2, pp.727-751
Data Type: article
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