APPLICATIONS OF A RELATIVE VARIATIONAL PRINCIPLE TO DIMENSIONS OF NONCONFORMAL EXPANDING MAPS

被引：6

作者：

Yayama, Yuki ^{[1
]}

机构：

[1] Univ Chile, Ctr Modelamiento Matemat, Santiago, Chile

来源：

STOCHASTICS AND DYNAMICS | 2011年 / 11卷 / 04期

关键词：

Relative pressure; relative variational principle; subadditive potential; symbolic dynamical systems; Hausdorff dimension; nonconformal expanding map; THERMODYNAMIC FORMALISM; EQUILIBRIUM STATES; PRESSURE;

D O I：

10.1142/S0219493711003486

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Zhao and Cao (2008) showed the relative variational principle for subadditive potentials in random dynamical systems. Applying their result, we find the Hausdorff dimension of an n (>= 3)-dimensional general Sierpinski carpet which has an irreducible sofic shift in symbolic representation and study an invariant ergodic measure of full Hausdorff dimension. These generalize the results of Kenyon and Peres (1996) on the Hausdorff dimension of an n-dimensional general Sierpinski carpet represented by a full shift.

引用

页码：643 / 679

页数：37

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