Cycles of polynomial mappings in several variables
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 \(N=1\).
scientific article; zbMATH DE number 624936