DYNAMICS OF THE p-ADIC SHIFT AND APPLICATIONS

被引：15

作者：

Kingsbery, James

Levin, Alex ^{[1
]}

Preygel, Anatoly ^{[1
]}

Silva, Cesar E. ^{[2
]}

机构：

[1] MIT, Cambridge, MA 02139 USA

[2] Williams Coll, Williamstown, MA 01267 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2011年 / 30卷 / 01期

基金：

美国国家科学基金会;

关键词：

Measure-preserving; ergodic; Bernoulli; shift; p-adic;

D O I：

10.3934/dcds.2011.30.209

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

There is a natural continuous realization of the one-sided Bernoulli shift on the p-adic integers as the map that shifts the coefficients of the p-adic expansion to the left. We study this map's Mahler power series expansion. We prove strong results on p-adic valuations of the coefficients in this expansion, and show that certain natural maps (including many polynomials) are in a sense small perturbations of the shift. As a result, these polynomials share the shift map's important dynamical properties. This provides a novel approach to an earlier result of the authors.

引用

页码：209 / 218

页数：10

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