A study is made of the behavior as k → ∞ of the iterations Tk(x) of a homogeneous polynomial transformation T acting from Rn to Rn according to the formula (T(x))i=Qi (x), i=1, 2,..., n, where Qi(x) is a homogeneous polynomial of degree m>1 with positive coefficients.
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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.
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Evstigneev, I.V. Iterations of homogeneous polynomial transformations with positive coefficients. Mathematical Notes of the Academy of Sciences of the USSR 6, 702–704 (1969). https://doi.org/10.1007/BF01093805
- Positive Coefficient
- Homogeneous Polynomial
- Polynomial Transformation