Asymptotic Hausdorff dimensions of Cantor sets associated with an asymptotically non-hyperbolic family

被引：4

作者：

Fan, AH ^{[1
]}

Jiang, YP

Wu, J

机构：

[1] Wuhan Univ, Dept Math, Wuhan 430072, Peoples R China

[2] Univ Picardie, CNRS, UMR 6140, LAMFA, F-80039 Amiens, France

[3] CUNY Queens Coll, Dept Math, Flushing, NY 11367 USA

[4] CUNY, Grad Sch, Dept Math, New York, NY 10016 USA

[5] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2005年 / 25卷

关键词：

D O I：

10.1017/S014338570500009X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The geometry of Cantor systems associated with an asymptotically non-hyperbolic family (f(epsilon))0 <=epsilon <=epsilon(0) was studied by Jiang (Geometry of Cantor systems. Trans. Amer Math. Soc. 351 (1999), 1975-1987). By applying the geometry studied there, we prove that the Hausdorff dimension of the maximal invariant set of f(epsilon), behaves like 1-K epsilon(1/gamma) asymptotically, as was conjectured by Jiang (Generalized Ulam-von Neumann transformations. PhD Thesis, CUNY Graduate Center, May 1999).

引用

页码：1799 / 1808

页数：10

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