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Journal of Complex Analysis
Volume 2017, Article ID 8474868, 7 pages
https://doi.org/10.1155/2017/8474868
Research Article

Uniqueness of the Sum of Points of the Period-Five Cycle of Quadratic Polynomials

Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, 80101 Joensuu, Finland

Correspondence should be addressed to Pekka Kosunen; if.feu@nenusok.akkep

Received 3 August 2017; Accepted 29 October 2017; Published 23 November 2017

Academic Editor: Arcadii Z. Grinshpan

Copyright © 2017 Pekka Kosunen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

It is well known that the sum of points of the period-five cycle of the quadratic polynomial 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 Gröbner-bases and especially extension theory from the theory of polynomial algebra.