On the iterations of certain maps \(X \mapsto K \cdot(X + X^{- 1})\) over finite fields of odd characteristic
type: Item
instance of: scholarly article
title: On the iterations of certain maps \(X \mapsto K \cdot(X + X^{- 1})\) over finite fields of odd characteristic
zbMATH Open document ID: 1317.37114
published in: Journal of Number Theory
publication date: 2014-08-29T00:00:00Z
full work available at URL: https://arxiv.org/abs/1304.3283
review text: This work is concerned with the dynamics of rational maps of the form \(k\cdot(x+x^{-1})\) over finite fields of odd characteristic. The dynamics is studied by considering the graph whose vertices are the elements of the field, and where an edge joins two vertices if the dynamics carries one vertex into the other. The author identifies a set of values of \(k\) (depending on the characteristic) for which a detailed description of such graphs is possible, extending a previous investigation for the case \(k=1\) over fields of characteristic 2, 3 and 5 [the author, ibid. 133, No. 4, 1207--1228 (2013; Zbl 1306.37102); Contemp. Math. 579, 187--204 (2012; Zbl 1302.37074)].
reviewed by: Franco Vivaldi
Mathematics Subject Classification ID: 37P05
Mathematics Subject Classification ID: 11T06
zbMATH DE Number: 6335922
zbMATH Keywords: dynamical systems
zbMATH Keywords: finite fields
zbMATH Keywords: arithmetic dynamics
zbMATH Keywords: elliptic curves
Wikidata QID: Q114157535
MaRDI profile type: Publication
OpenAlex ID: W1645919873
arXiv ID: 1304.3283
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DOI: 10.1016/J.JNT.2014.02.024
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author: S. Ugolini
description: scientific article; zbMATH DE number 6335922