多项式型迭代方程的多项式解

Abstract

Abstract:

Most of known results for the polynomial-like iterative equation were given for monotone functions. In this paper, we discuss this equation for a polynomial function, which is non-monotonic. In one-dimensional case, we apply the method of computer algebra system SINGULAR decomposing algebraic varieties to find a sufficient and necessary condition for the polynomial-like iterative equation of orders 2 and 3 having quadratic polynomial solutions respectively and give quadratic polynomial solutions of both two equations. Then we give a procedure for computing polynomial solutions of the polynomial-like equation. In two-dimensional case, applying the idea of one-dimensional case we obtain several sufficient and necessary conditions for second order polynomial-like iterative equation having quadratic degree-preserving polynomial solutions when the given function is a two-dimensional homogeneous polynomial mapping of degree 2.

Key words: Polynomial-like iterative equation, Leading Coefficient Problem, Polynomial solutions, Algebraic variety, Minimal irreducible decomposition

CLC Number:

O193

Zhiheng Yu,Xiaobing Gong. Polynomial Solutions of the Polynomial-Like Iterative Equation[J].Acta mathematica scientia,Series A, 2019, 39(6): 1352-1364.

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Polynomial Solutions of the Polynomial-Like Iterative Equation

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