具有旋转对称根的多项式的牛顿映照

摘要

主要研究特殊多项式的牛顿映照的动力学性质。通过研究根的分布和重数，揭示了当多项式的根关于某点具有一定的旋转对称性，且对称根的重数都相同时，此类多项式的牛顿映照要么是双曲的，要么是次双曲的。另外多项式的牛顿映照的动力学性质为多项式的某些问题提供了新的思路。%　　The dynamical properties of Newton maps for special polynomials are investigated. Analysis of the distribution and multiplicities of roots revealed that Newton maps for polynomials, whose roots are some rotationally symmetric with a fixed point and the multiplicities of symmetric roots are all the same, are either hyperbolic or subhyperbolic. Moreover, the study of dynamical properties of Newton maps for polynomials produce new ideas for some problems of polynomials.