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arXiv · 1803.09481

Uniqueness of the sum of points of the period five cycle of quadratic polynomials

Pekka Kosunen
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Abstract

It is well known that the sum of points of the period five cycle of the quadratic polynomial $f_{c}(x)=x^{2}+c$ is generally not one-valued. In this paper we will show that the sum of cycle points of the curves of period five is at most three-valued on a new coordinate plane, and that this result is essentially the best possible. The method of our proof relies on a implementing Gr\"obner-bases and especially extension theory from the theory of polynomial algebra.

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Pekka Kosunen. 2018-03-26. Uniqueness of the sum of points of the period five cycle of quadratic polynomials. https://arxiv.org/abs/1803.09481

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