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Using van der Put basis to determine if a 2-adic function is measure-preserving or ergodic w.r.t. Haar measure
Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics. (mathematical modeling)ORCID iD: 0000-0002-9857-0938
Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.ORCID iD: 0000-0003-1919-1495
2011 (English)In: Advances in Non-Archimedean Analysis: 11th International Conference p-adic Funcional Analysis, July 5-9, 2010, Université Blaise Pascal, Clemont-Ferrand, France / [ed] Jesus Araujo-Gomez, Bertin Diarra and Alain Escassut, American Mathematical Society (AMS), 2011, Vol. 551, 33-38 p.Chapter in book (Refereed)
Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2011. Vol. 551, 33-38 p.
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-16578DOI: 10.1090/conm/551ISBN: 978-0-8218-5291-0 (p) ISBN: 978-0-8218-8230-6 (e) OAI: oai:DiVA.org:lnu-16578DiVA: diva2:472854
Available from: 2012-01-04 Created: 2012-01-04 Last updated: 2016-05-03Bibliographically approved
In thesis
1. P-adic dynamical systems and van der Put basis technique
Open this publication in new window or tab >>P-adic dynamical systems and van der Put basis technique
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Theory of dynamical systems in fields of p-adic numbers is  an important part of algebraic and arithmetic dynamics. The study of p-adic dynamical systems is motivated by their applications in various areas of mathematics, e.g., in physics, genetics, biology, cognitive science, neurophysiology, computer science, cryptology, etc.

In particular, p-adic dynamical systems found applications in cryptography, which stimulated the interest to nonsmooth dynamical maps. An important class of (in general) nonsmooth maps is given by 1-Lipschitz functions.

In this thesis we restrict our study to the class of 1-Lipschitz functions and describe measure-preserving (for the Haar measure on the ring of p-adic integers) and ergodic functions.

The main mathematical tool used in this work is the representation of the function by the van der Put series which is actively used in p-adic analysis. The van der Put basis differs fundamentally from previously used ones (for example, the monomial and Mahler basis)  which are related to the algebraic structure of p-adic fields. The basic point in the construction of van der Put basis is the continuity of the characteristic function of a p-adic ball.

Also we use an algebraic structure (permutations) induced by coordinate functions with partially frozen variables.

In this thesis, we present a description of 1-Lipschitz measure-preserving and ergodic functions for arbitrary prime p.

Place, publisher, year, edition, pages
Växjö: Linnaeus University Press, 2013
Series
Linnaeus University Dissertations, 140/2013
Keyword
dynamical systems, p-adic, 1-Lipschitz, measure-preserving, ergodicity, spheres, uniformly differentiable
National Category
Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-28026 (URN)978-91-87427-37-4 (ISBN)
Public defence
2013-08-27, D1136, Vaxjo, 13:00 (English)
Opponent
Supervisors
Available from: 2013-09-10 Created: 2013-08-10 Last updated: 2015-10-12Bibliographically approved

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
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  • Other locale
More languages
Output format
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  • asciidoc
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