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Iterations of homogeneous polynomial transformations with positive coefficients

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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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Literature cited

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    S. Ulam, Unsolved Problems in Mathematics [Russian translation], Moscow (1964).

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    P. R. Stein and S. M. Ulam, A Study of Certain Combinatorial Problems Through Experiments on Computing Machines. Proceedings of the High Speed Computer Conference, Louisiana State University, Baton Rouge (1955).

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    P. R. Stein and S. M. Ulam, Quadratic Transformations, Part I. Los Alamos Scientific Laboratory Report No. 2305, Office of Technical Services, US Department of Commerce, Washington 25, D. C.

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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).

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  • Positive Coefficient
  • Homogeneous Polynomial
  • Polynomial Transformation