Criteria of measure-preserving for p-adic dynamical systems in terms of the van der Put basis

JOURNAL OF NUMBER THEORY

卷:133

Article

Khrennikov, Andrei¹  Yurova, Ekaterina¹ 

[1] Linnaeus Univ, Int Ctr Math Modelling Phys & Cognit Sci, S-35195 Vaxjo, Sweden

关键词: p-Adic numbers;    Van der Put basis;    Dynamics;    Haar measure;    Measure-preserving;   

DOI  :  10.1016/j.jnt.2012.08.013

来源: Elsevier

【 摘 要 】

This paper is devoted to (discrete) p-adic dynamical systems, an important domain of algebraic and arithmetic dynamics. We consider the following open problem from theory of p-adic dynamical systems. Given continuous function f : Z(p) -> Z(p). Let us represent it via special convergent series, namely van der Put series. How can one specify whether this function is measure-preserving or not for an arbitrary p? In this paper, for any prime p, we present a complete description of all compatible measure-preserving functions in the additive form representation. In addition we prove the criterion in terms of coefficients with respect to the van der Put basis determining whether a compatible function f : Z(p) -> Z(p) preserves the Haar measure. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free