实非吸性不动点猜想及其超越
The real non-attractive fixed point conjecture and beyond
摘要：
是否每个次数至少为2的多项式P都有一个不动点z 0，其乘数的实部大于或等于1，即，（P '（z 0））的实部> 1？这个问题，提出了Coelho和Kalantari在多少真正的吸性不动点可以多项式？Math.Gaz.103（2019），no.556，65{76. [3]不仅对所有多项式，而且对所有具有超吸引不动点的有理函数，都给出了肯定的回答。然而，这并不适用于所有的有理函数。进一步研究了不动点乘子的分布。给出了乘子实部均为实部1的二次和三次多项式的特征。本文给出了三次多项式和四次多项式的乘子都等距的一个充要条件：是否每次至少为2的多项式P都有一个不动点z 0，其乘子的实部大于或等于1，即，P '（z 0）的实部> 1？这个问题，提出了Coelho和Kalantari在多少真正的吸性不动点可以多项式？Math.Gaz.103（2019），no.556，65{76. [3]不仅对所有多项式，而且对所有具有超吸引不动点的有理函数，都给出了肯定的回答。然而，这并不适用于所有的有理函数。进一步研究了不动点乘子的分布。给出了乘子实部均为实部1的二次和三次多项式的特征。找到了三次和四次多项式的乘子与1等距的一个充要条件。
英文摘要：
Is it always true that every polynomial P with the degree at least two has a fixed point z0, the real part of whose multiplier is bigger than or equal to 1, i.e., Real part of (P'(z0))> 1? This question, raised by Coelho and Kalantari in How many real attractive fixed points can a polynomial have? Math. Gaz. 103 (2019), no. 556, 65{76. [3] is answered affirmatively not only for all polynomials but also for all rational functions with a super attracting fixed point. However, this is not true for all rational functions. Some further investigation on distribution of multipliers of fixed points is made. Quadratic and cubic polynomials, all of whose multipliers have real part 1 are characterized. A necessary and sufficient condition is found for cubic and quartic polynomials, all of whose multipliers are equidistant from Is it always true that every polynomial P with the degree at least two has a fixed point z0, the real part of whose multiplier is bigger than or equal to 1, i.e., Real part of P'(z0)> 1? This question, raised by Coelho and Kalantari in How many real attractive fixed points can a polynomial have? Math. Gaz. 103 (2019), no. 556, 65{76. [3] is answered affirmatively not only for all polynomials but also for all rational functions with a super attracting fixed point. However, this is not true for all rational functions. Some further investigation on the distribution of multipliers of fixed points is made. Quadratic and cubic polynomials, all of whose multipliers have real part 1 are characterized. A necessary and sufficient condition is found for cubic and quartic polynomials, all of whose multipliers are equidistant from 1.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
