lnu.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
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
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Van der Put basis and p-adic dynamics
Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.ORCID iD: 0000-0003-1919-1495
2010 (English)In: P-Adic Numbers, Ultrametric Analysis, and Applications, ISSN 2070-0466, E-ISSN 2070-0474, Vol. 2, no 2, p. 175-178Article in journal (Other academic) Published
Place, publisher, year, edition, pages
MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC. , 2010. Vol. 2, no 2, p. 175-178
Keywords [en]
van der Put basis, p-adic dynamical systems, ergodicity
National Category
Other Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-9991DOI: 10.1134/S207004661002007XOAI: oai:DiVA.org:lnu-9991DiVA, id: diva2:387724
Available from: 2011-01-14 Created: 2011-01-14 Last updated: 2017-12-11Bibliographically 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
Keywords
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

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full texthttp://www.springerlink.com/content/u9648xm41468x523/

Authority records BETA

Yurova, Ekaterina

Search in DiVA

By author/editor
Yurova, Ekaterina
By organisation
School of Computer Science, Physics and Mathematics
In the same journal
P-Adic Numbers, Ultrametric Analysis, and Applications
Other Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 80 hits
CiteExportLink to record
Permanent link

Direct link
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
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf