Dimension Theory and Fuchsian Groups

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• 作者：Alejandro Meson
  Fernando Vericat
  
• 关键词：dimension theory ; multifractal analysis ; boundary hyperbolic maps
• 刊名：Acta Applicandae Mathematicae
• 出版年：2004
• 出版时间：January 2004
• 年：2004
• 卷：80
• 期：1
• 页码：95-121
• 全文大小：204KB
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• 作者单位：Alejandro Meson
  Fernando Vericat
  
  
• ISSN：1572-9036

文摘

In this paper we review some concepts of Dimension Theory in Dynamical Systems and we show how to apply them for studying growth rates of Kleinian groups acting on the hyperbolic plane H 2. The mainly focus on: multifractal analysis, additive and nonadditive thermodynamic formalisms and Gibbs states. In order to connect these concepts with groups we define a family of potentials 蠒 n (尉):=d h (O,e 0 e 1...e n (O)), 尉鈭埼?(the limit set of 螕), where d h is the hyperbolic metric in H 2 and e 0 e 1... is a sequence in the generators of 螕 assigned to 尉. These sequences are obtained from the method by C. Series for coding hyperbolic geodesics. Next, a decomposition in level sets K 伪:={尉:lim鈥?sub class="a-plus-plus"> n鈫掆垶 $\frac{{d_h (0,e_0 e_1 ...e_n (0))}}{n}$ =伪} is considered and a variational multifractal analysis of the entropy spectrum of K 伪, by means of the formalism developed by Barreira, is done.