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On the dynamics of \(\varphi : x \rightarrow x^p + a\) in a local field. (English) Zbl 1474.37136
Summary: Let \(K\) be a local field, \(a \in K\) and \(\varphi : x \rightarrow x^p + a\) where \(p\) denotes the characteristic of the residue field. We prove that the minimal subsets of the dynamical system \((K, \varphi)\) are cycles and describe the cycles of this system.
MSC:
37P20 Dynamical systems over non-Archimedean local ground fields
37P05 Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps
11F85 \(p\)-adic theory, local fields
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[1] D. Adam and Y. Fares, On two like-affine dynamical systems in a local field, preprint. · Zbl 1273.37046
[2] A.-H. Fan and Y. Fares, Minimal subsystems of affine dynamics on local fields, \(Arch. Math.\)96 (2011), 423-434. · Zbl 1214.11134
[3] Y. Fares, Factorial preservation, \(Arch. Math.\)83 (2004), 497-506. | Copyright Cellule MathDoc 2018 · Zbl 1073.13011
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