Adam, David; Fares, Youssef On the dynamics of \(\varphi : x \rightarrow x^p + a\) in a local field. (English) Zbl 1474.37136 Actes Rencontres C.I.R.M. 2, No. 2, 81-85 (2010). 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 Keywords:residue field; local fields; cycle × Cite Format Result Cite Review PDF Full Text: DOI References: [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.