Natural extensions for p-adic β-shifts and other scaling maps

被引：3

作者：

Furno, Joanna ^{[1
]}

机构：

[1] De Paul Univ, Dept Math Sci, 2320 N Kenmore Ave, Chicago, IL 60614 USA

来源：

INDAGATIONES MATHEMATICAE-NEW SERIES | 2019年 / 30卷 / 06期

关键词：

beta-shift; Locally scaling; p-adic; Natural extension; Isometry; INVARIANT DENSITIES; TRANSFORMATIONS;

D O I：

10.1016/j.indag.2019.08.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The p-adic beta-shift can naturally be thought of as an isometry on the p-adic integers (multiplication by a unit), followed by an iterate of the one-sided shift. We show that all (p(-n), p(n))-locally scaling maps have such a decomposition into an iterate of the one-sided shift composed with an isometry. We then use this decomposition to give a formula for the natural extension. (C) 2019 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

引用

页码：1099 / 1108

页数：10

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