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On recent results of ergodic property for p-adic dynamical systems
Linnaeus University, Faculty of Technology, Department of Mathematics.ORCID iD: 0000-0003-1919-1495
2014 (English)In: P-Adic Numbers, Ultrametric Analysis, and Applications, ISSN 2070-0466, E-ISSN 2070-0474, Vol. 6, no 3, 235-257 p.Article in journal (Refereed) Published
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, 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 paper we present a recent summary of results about 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.

Place, publisher, year, edition, pages
Pleiades Publishing , 2014. Vol. 6, no 3, 235-257 p.
Keyword [en]
dynamical systems, p-adic, 1-Lipschitz, measure-preserving, ergodicity, spheres, uniformly differentiable
National Category
Algebra and Logic
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-36328DOI: 10.1134/S2070046614030066OAI: oai:DiVA.org:lnu-36328DiVA: diva2:736920
Available from: 2014-08-11 Created: 2014-08-11 Last updated: 2015-10-12Bibliographically approved

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Yurova Axelsson, Ekaterina
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CiteExportLink to record
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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
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  • Other locale
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