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Scientific Object Identifier: http://s-o-i.org/1.1/TAS-10-102-30
DOI: https://dx.doi.org/10.15863/TAS.2021.10.102.30
Language: English
Citation: Abdukaxorova, Z. T. (2021). About non-Archimedian function dynamical system. ISJ Theoretical & Applied Science, 10 (102), 413-418. Soi: http://s-o-i.org/1.1/TAS-10-102-30 Doi: https://dx.doi.org/10.15863/TAS.2021.10.102.30 |
Pages: 413-418
Published: 30.10.2021
Abstract: In this paper we consider the discrete time ?? -adic dynamic system of the family of rational functions in the form 1 ?? 2 +?? . In order to solve the problem in this study, a number of real non-negative functions were constructed using the properties of the ?? -adic norm and some substitutions.The following conclusions were drawn about the discrete time dynamics of p-adic rational functions under consideration using their results by studying their dynamics: This rational function cannot have a unique fixed point, the parameter ?? has two fixed points at a single value of ??=? 3 3 4 , and the parameter ?? has three fixed points at the values of ???? 3 3 4 proved to be. The ?? -adic dynamical system with two fixed points was studied at ??=2. Conditions were found for the parameters that attractor and indifferent fixed points. Also, basin of attraction, Siegel disks were found and trajectories were studied.
Key words: ?? -adic norm,fixed point, attractor fixed point, basin of attraction, indifferent fixed point, Siegel disk, a maximum Siegel disk (SI((x)), 2-adic norm, open ball, closed ball, sphere.
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