三次多项式的非单调高度  

Non-monotonicity height for cubic polynomials

作　　者：包军元 BAO Junyuan(School of Mathematics,Sichuan University,Chengdu,Sichuan 610064,China)

机构地区：[1]四川大学数学学院,四川成都610064

出　　处：《内江师范学院学报》2023年第4期42-46,共5页Journal of Neijiang Normal University

摘　　要：非单调高度通过描述非单调连续函数在迭代下非单调点个数的变化来刻画函数在迭代下的复杂程度.前人已经证明二次多项式这类特殊的连续函数的高度或者是1或者是无穷,即随着迭代次数的增加其非单调点的个数或者恒为1或者单增到无穷,并对单增到无穷的情形计算非单调点个数变化时的参数,猜测当参数μ<μ_(7.5)时非单调点个数按2^(n)-1增长.本文研究了三次多项式函数的非单调高度,证明其高度或者是0或者是无穷.另外对二次多项式否定了前人提出的猜测.Non-monotonicity height describes complexity of a non-monotonic continuous function under iteration by presenting the change of the number of non-monotonic points of the function under iteration.It was proved that the height of any quadratic polynomial,a special continuous function,is either 1 or infinity,i.e.,the number of non-monotonic points is either constant 1 or increases to infinity as the number of iteration increases.For the latter case,they calculated the parameters at which the number of non-monotonic points varies and conjectures that the number of non-monotonic points increases in the law 2^(n)-1 for parameterμ<μ_(7.5).and that the non-monotonic height for cubic polynomials is investigated and the height is proved either 0 or infinity.Additionally,a negative answer is given to the predecessors'conjecture for quadratic polynomials.

关 键 词：多项式 迭代 非单调高度 拓扑共轭 

分 类 号：O192[理学—数学]