Cycles of polynomial mappings in several variables
type: Item
instance of: scholarly article
title: Cycles of polynomial mappings in several variables
zbMATH Open document ID: 0804.11059
DOI: 10.1007/BF02567614
published in: Manuscripta Mathematica
publication date: 1995-01-24T00:00:00Z
full work available at URL: https://eudml.org/doc/155961
review text: Let \(R\) be a discrete valuation domain of zero characteristic and with finite residue field. It is shown that there exists an upper bound for the length of a finite cyclic orbit of any mapping \(R^ N \to R^ N\) defined by a system of polynomials over \(R\). This bound is given explicitly and depends only on \(R\) and \(N\). This implies a corresponding bound in the case when \(R\) is the ring of integers of an algebraic number field \(K\). Here the bound depends only on \(N\) and the degree of \(K\). This generalizes previous results of the author [Acta Arith. 66, 11--22 (1994; Zbl 0803.11063)] dealing with the case \(N=1\).
Mathematics Subject Classification ID: 37P05
Mathematics Subject Classification ID: 37P20
Mathematics Subject Classification ID: 11S05
Mathematics Subject Classification ID: 37P35
Mathematics Subject Classification ID: 13F30
Mathematics Subject Classification ID: 14E05
zbMATH DE Number: 624936
zbMATH Keywords: polynomial maps
zbMATH Keywords: periodic points
zbMATH Keywords: finite orbits
author: Tadeusz Pezda
reviewed by: Władysław Narkiewicz
MaRDI profile type: Publication
cites work: The existence of fixpoints of entire functions
cites work: Fixpoints of Polynomials and Rational Functions
cites work: Invariant sets of morphisms on projective and affine number spaces
cites work: Q5181781
cites work: On polynomial transformations in several variables
cites work: Polynomial cycles in algebraic number fields
cites work: Periodic points on an algebraic variety
cites work: Polynomial cycles in certain local domains
cites work: Cycles of polynomials in algebraically closed fields of positive characteristic
description: scientific article; zbMATH DE number 624936