Real cross section of the connectedness locus of the family of polynomials (z^2^n^+^1 + a)^2^n^+^1 + b

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  • 多項式族 (z^2^n^+^1 + a)^2^n^+^1 + bの連結性集合の実断面

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Abstract

Yeshun Sun & Yongcheng Yin [3] and H. Ishida & T. Itoh [2] presented a precise description of the real cross section of the connectedness locus of the family of bi-quadratic polynomials {(z^2+a)^2+b}. In this note, we shall give a precise description of the real cross section of the connectedness locus of the family of polynomials {(P_2_n_+_1,b ◦ P_2_n_+_1,a)(z)} = {(z^2^n^+^1 +a)^2^n^+^1 +b}, where a, b are complex numbers and n is a positive integer. Our proof is an elementary one.

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