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Criteria of measure-preserving for p-adic dynamical systems in terms of the van der Put basisPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2013 (English)In: Journal of Number Theory, ISSN 0022-314X, E-ISSN 1096-1658, Vol. 133, no 2, 484-491 p.Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2013. Vol. 133, no 2, 484-491 p.
##### Keyword [en]

p-Adic numbers, Van der Put basis, Dynamics, Haar measure, Measure-preserving
##### National Category

Mathematics
##### Research subject

Mathematics, Mathematics
##### Identifiers

URN: urn:nbn:se:lnu:diva-23526DOI: 10.1016/j.jnt.2012.08.013ISI: 000311769200009OAI: oai:DiVA.org:lnu-23526DiVA: diva2:589442
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Available from: 2013-01-18 Created: 2013-01-18 Last updated: 2016-05-03Bibliographically approved
##### In thesis

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.

1. P-adic dynamical systems and van der Put basis technique$(function(){PrimeFaces.cw("OverlayPanel","overlay639865",{id:"formSmash:j_idt1380:0:j_idt1384",widgetVar:"overlay639865",target:"formSmash:j_idt1380:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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