论文标题
真正的非吸引固定点猜想及以后
The real non-attractive fixed point conjecture and beyond
论文作者
论文摘要
每个具有至少两个程度的多项式P具有固定点Z0，其乘数的实际部分大于或等于1，即（p'（z0））> 1的实际部分？这个问题是由Coelho和Kalantari提出的多项式可以有多少个真正有吸引力的固定点？数学。加兹。 103（2019），没有。 556，65 {76。 [3]不仅对所有多项式，而且对具有超级吸引固定点的所有理性函数肯定。但是，对于所有理性功能，这并不是如此。对固定点的乘数分布进行了进一步的研究。二次和立方多项式，其所有乘数具有实际部分1。对于立方体和四分之一的多项式，发现了必要且充分的条件，所有乘数都与之相等的是，每个多项式p的每个多项式P具有至少两个的次数p，其乘数具有固定点Z0，其乘数的真实部分大于或等于1，即P'（z0）> 1> 1？这个问题是由Coelho和Kalantari提出的多项式可以有多少个真正有吸引力的固定点？数学。加兹。 103（2019），没有。 556，65 {76。 [3]不仅对所有多项式，而且对具有超级吸引固定点的所有理性函数肯定。但是，对于所有理性功能，这并不是如此。对固定点的乘数分布进行了进一步的研究。二次和立方多项式，其所有乘数具有实际部分1。对于立方和四分之一的多项式发现了必要且充分的条件，其所有乘数都与1相等。
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.
