On the Hausdorff dimension of the recurrent sets induced from endomorphisms of free groups

被引：0

作者：

Ishii, Yutaka ^{[1
]}

Oka, Tatsuya ^{[2
]}

机构：

[1] Kyushu Univ, Dept Math, Nishi Ku, Motooka 744, Fukuoka 8190395, Japan

[2] Fujitsu Ltd, Fujitsu Res, Data & Secur Res Lab, Nakahara Ku, Kawasaki, Kanagawa 2118588, Japan

来源：

JOURNAL OF FRACTAL GEOMETRY | 2022年 / 9卷 / 1-2期

关键词：

Recurrent set; Hausdorff dimension; Markov partition; MARKOV PARTITIONS;

D O I：

10.4171/JFG/120

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that F. Dekking's recurrent sets in R-2, which correspond to Markov partitions for conformally expanding maps of the 2-torus, have Hausdorff dimension strictly greater than one. This is a counterpart to the classical result of R. Bowen on the non-smoothness of the Markov partitions for Anosov diffeomorphisms of the 3-torus. We also present a non-conformal example where the recurrent set is a parallelogram and hence its Hausdorff dimension is one.

引用

页码：171 / 192

页数：22

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