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On computation for the multipliers of periodic orbits of polynomial maps. (English) Zbl 0919.58053
Summary: Today the calculation by a computer plays a more and more important role in the iteration theory of functions. The present paper is concerned with the study of the computations with polynomial maps whose coefficients are included in an algebraic number field. Very recently, F. Vivaldi and S. Hatjispyros have given an algorithm to compute the multipliers of periodic orbits of a polynomial without computing the orbits themselves under some hypothesis. The authors show that these hypotheses are unnecessary, or equivalently they remove the hypothesis and show that the algorithm given by Vivaldi and Hatjispyros is still effective.
37F99 Dynamical systems over complex numbers
11R32 Galois theory
12F10 Separable extensions, Galois theory