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Study of ergodicity of *p*-adic dynamical systems with the aid of 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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2011 (English)Licentiate thesis, comprehensive summary (Other academic)
##### Abstract [en]

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

Växjö: Linnaeus University , 2011.
##### Keywords [en]

p-adic numbers, van der Put basis, 1-Lipschitz, measure-preserving, ergodicity, sphere, T-function
##### National Category

Other Mathematics
##### Research subject

Mathematics, Applied Mathematics
##### Identifiers

URN: urn:nbn:se:lnu:diva-15821Libris ID: 12516256OAI: oai:DiVA.org:lnu-15821DiVA, id: diva2:456780
##### Presentation

2011-09-27, 13:15 (English)
##### Opponent

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##### Funder

Swedish Research CouncilAvailable from: 2012-01-30 Created: 2011-11-15 Last updated: 2017-09-01Bibliographically approved
##### In thesis

The study of *p*-adic dynamical systems is motivated by their applications in various (and surprisingly diverse) areas of mathematics, e.g., in physics, genetics, biology, cognitive science, neurophysiology, computer science, cryptology, etc.

In this thesis we use decomposition of a continuous function f : zp -> zp into a convergent van der Put series to determine whether f is 1-Lipschitz, measure-preserving and/or ergodic.

The main mathematical tool used in this research is the representation of the function by the van der Put series, which are special convergent series from *p*-adic analysis.

This is the first attempt to use the van der Put basis to examine the properties of (discrete) dynamical systems in fields of *p*-adic numbers. Note that the van der Put basis differs fundamentally from previously used ones, for example, the monomial and Mahler bases, which are related to the algebraic structure of *p*-adic fields.

The van der Put basis is related to the zero dimensional topology of these fields (ultrametric structure), since it consists of characteristic functions of *p*-adic balls; i.e., the basic point in the construction of this basis is the continuity of the characteristic function of a *p*-adic ball.

1. P-adic dynamical systems and van der Put basis technique$(function(){PrimeFaces.cw("OverlayPanel","overlay639865",{id:"formSmash:j_idt1313:0:j_idt1322",widgetVar:"overlay639865",target:"formSmash:j_idt1313:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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