Tuning and plateaux for the entropy of α-continued fractions

被引：18

作者：

Carminati, Carlo ^{[1
]}

Tiozzo, Giulio ^{[2
]}

机构：

[1] Univ Pisa, Dipartimento Matemat, I-56127 Pisa, Italy

[2] Harvard Univ, Dept Math, Cambridge, MA 02138 USA

来源：

NONLINEARITY | 2013年 / 26卷 / 04期

关键词：

D O I：

10.1088/0951-7715/26/4/1049

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The entropy h(T-alpha) of alpha-continued fraction transformations is known to be locally monotone outside a closed, totally disconnected set epsilon. We will exploit the explicit description of the fractal structure of epsilon to investigate the selfsimilarities displayed by the graph of the function alpha bar right arrow h(T-alpha). Finally, we completely characterize the plateaux occurring in this graph, and classify the local monotonic behaviour.

引用

页码：1049 / 1070

页数：22

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