Julia sets of the Schroder iteration functions of a class of one-parameter polynomials with high degree

摘要

In this paper the theory of Julia sets of Schroder iteration functions is introduced, the Julia sets of the Schroder functions of a one-parameter family polynomials with high degree are constructed through iteration method, and their structures are analyzed. Consequently, the following results are found in the study: (1) the Julia sets of the Schroder iteration functions of a one-parameter family polynomials with high degree contain the structure of classical Mandelbrot-like set; (2) the orbits of the critical points may escape from the zero points of the corresponding polynomial to converge to the k-cycle attractive basin or the extra fixed points; (3) if critical points on parameter plane are selected to construct Julia sets on dynamics plane, then attractive k-cycle basin will emerge, while it will not emerge if no critical points are selected; (4) the extra fixed points may be repulsive, litmusless or attractive, but the former takes the major role and (5) the Julia sets of the Schroder iteration functions have symmetry. (c) 2005 Elsevier Inc. All rights reserved.