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Teoreticheskaya i Matematicheskaya Fizika, 1998, Volume 114, Number 3, Pages 349–365
DOI: https://doi.org/10.4213/tmf845
(Mi tmf845)
 

This article is cited in 45 scientific papers (total in 45 papers)

$p$-Adic dynamic systems

S. A. Albeverioa, B. Tirozzib, A. Yu. Khrennikovc, S. de Smedtd

a University of Bonn, Institute for Applied Mathematics
b University of Rome "La Sapienza"
c Växjö University
d Vrije Universiteit
Abstract: Dynamic systems in non-Archimedean number fields (i. e. fields with non-Archimedean valuations) are studied. Results are obtained for the fields of $p$-adic numbers and complex $p$-adic numbers. Simple $p$-adic dynamic systems have a very rich structure–attractors, Siegel disks, cycles, and a new structure called a “fuzzy cycle”. The prime number $p$ plays the role of a parameter of the $p$-adic dynamic system. Changing $p$ radically changes the behavior of the system: attractors may become the centers of Siegel disks, and vice versa, and cycles of different lengths may appear or disappear.
Received: 28.08.1997
English version:
Theoretical and Mathematical Physics, 1998, Volume 114, Issue 3, Pages 276–287
DOI: https://doi.org/10.1007/BF02575441
Bibliographic databases:
Language: Russian
Citation: S. A. Albeverio, B. Tirozzi, A. Yu. Khrennikov, S. de Smedt, “$p$-Adic dynamic systems”, TMF, 114:3 (1998), 349–365; Theoret. and Math. Phys., 114:3 (1998), 276–287
Citation in format AMSBIB
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\by S.~A.~Albeverio, B.~Tirozzi, A.~Yu.~Khrennikov, S.~de Smedt
\paper $p$-Adic dynamic systems
\jour TMF
\yr 1998
\vol 114
\issue 3
\pages 349--365
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\crossref{https://doi.org/10.4213/tmf845}
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\zmath{https://zbmath.org/?q=an:0974.37018}
\transl
\jour Theoret. and Math. Phys.
\yr 1998
\vol 114
\issue 3
\pages 276--287
\crossref{https://doi.org/10.1007/BF02575441}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000075184200003}
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  • https://www.mathnet.ru/eng/tmf845
  • https://doi.org/10.4213/tmf845
  • https://www.mathnet.ru/eng/tmf/v114/i3/p349
  • This publication is cited in the following 45 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Теоретическая и математическая физика Theoretical and Mathematical Physics
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