关于一类非线性差分方程的解的频率收敛分析

Frequent convergence for solutions of a class of nonlinear difference equation

利用数列的频率测度定义及其性质,研究一类差分方程x2n+1=m-x n在3<m<1时的解4的频率收敛性。定义与所讨论差分方程密切相关的多项式函数,求出此函数的不动点,利用此函数在不同区间上的单调性,证明初始值取在区间[-1-4m-3(1/2)/2,1-1+4m(1/2)/2)∪(1-1+4m(1/2)/2,-1+4m-3(1/2)/2][1-4m-3(1/2)/2,-1+4m(1/2)/2)∪(-1+1+4m(1/2)/2,1+4m-3(1/2)/2]中时,差分方程的解有两个0.5度频率极限1+4m-3(1/2)/2和1-4m-3(1/2)/2。

Frequently convergence for solutions of a class of difference equation x n ＋ 1= m- x^2 nare dis-3cussed where m 1 by using definition and properties of frequency measure of real valued se-4quences. First of all,a polynomial function closely related to the difference equation is defined,and then its fixed points are presented. Finally,using monotone properties of this function in different interval,it[- 1- 4mis proved that if the initial values are in the interval [-1-√4m-3/2,1-√1＋4m/2）∪（1-√1＋4m/2,-1＋√4m-3/2][1-√4m-3/2,-1＋4m/2）∪（-1＋√1＋4m/2,1＋4m,-1＋√4m-3/2],then the solutions of the difference equation have two frequent limits 1＋√4m-3/2 and 1-√4m-3/2 of degree 0. 5.