Iterations of homogeneous polynomial transformations with positive coefficients

A study is made of the behavior as k of the iterations T^k(x) of a homogeneous polynomial transformation T acting from Rⁿ to Rⁿ according to the formula (T(x))_i=Q_i (x), i=1, 2,..., n, where Q_i(x) is a homogeneous polynomial of degree m>1 with positive coefficients.Translated from Matematicheskie Zametki, Vol. 6, No. 4, pp. 411–416, October, 1969.In conclusion I should like to thank S. A. Molchanov for proposing the topic and S. M. Natanzon for his help with the paper.