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Criteria of ergodicity for p-adic dynamical systems in terms of coordinate functions
Linnaeus University, Faculty of Technology, Department of Mathematics.ORCID iD: 0000-0002-9857-0938
Linnaeus University, Faculty of Technology, Department of Mathematics.ORCID iD: 0000-0003-1919-1495
2014 (English)In: Chaos, Solitons & Fractals, ISSN 0960-0779, E-ISSN 1873-2887, Vol. 60, p. 11-30Article in journal (Refereed) Published
Abstract [en]

This paper is devoted to the problem of ergodicity of p-adic dynamical systems. We solved the problem of characterization of ergodicity and measure preserving for (discrete) p-adic dynamical systems for arbitrary prime p for iterations based on 1-Lipschitz functions. This problem was open since long time and only the case p = 2 was investigated in details. We formulated the criteria of ergodicity and measure preserving in terms of coordinate functions corresponding to digits in the canonical expansion of p-adic numbers. (The coordinate representation can be useful, e.g., for applications to cryptography.) Moreover, by using this representation we can consider non-smooth p-adic transformations. The basic technical tools are van der Put series and usage of algebraic structure (permutations) induced by coordinate functions with partially frozen variables. We illustrate the basic theorems by presenting concrete classes of ergodic functions. As is well known, p-adic spaces have the fractal (although very special) structure. Hence, our study covers a large class of dynamical systems on fractals. Dynamical systems under investigation combine simplicity of the algebraic dynamical structure with very high complexity of behavior.

Place, publisher, year, edition, pages
2014. Vol. 60, p. 11-30
Keywords [en]
Ergodicity, dynamical systems, van der Put, coordinate functions
National Category
Mathematics
Research subject
Mathematics, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-34076DOI: 10.1016/j.chaos.2014.01.001ISI: 000333719000002Scopus ID: 2-s2.0-84893440046OAI: oai:DiVA.org:lnu-34076DiVA, id: diva2:715395
Available from: 2014-05-05 Created: 2014-05-05 Last updated: 2017-12-05Bibliographically approved

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Khrennikov, AndreiYurova, Ekaterina

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