[1]张晏志,郑穗生*.带有高斯取整函数的两个非线性三项递推关系的周期性[J].延边大学学报(自然科学版),2014,40(01):1-7.
　ZHANG Yanzhi,ZHENG Suisheng*.Periodicity of two nonlinear three term recurrence relations involving the Gauss bracket function[J].Journal of Yanbian University,2014,40(01):1-7.
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带有高斯取整函数的两个非线性三项递推关系的周期性

《延边大学学报(自然科学版)》[ISSN:1004-4353/CN:22-1191/N] 卷: 第40卷 期数: 2014年01期 页码: 1-7 栏目: 基础科学研究 出版日期: 2014-03-20
Title:
Periodicity of two nonlinear three term recurrence relations involving the Gauss bracket function
作者:
张晏志1;  郑穗生2*
1.台湾清华大学 工业工程与工程管理学系; 2.台湾清华大学 数学系: 台湾 新竹 30043
Author(s):
ZHANG Yanzhi1;  ZHENG Suisheng2*
1.Department of Industrial Engineering and Industrial Management, Tsinghua University; 2.Department of Mathematics, Tsinghua University: Hsinchu 30043, China
关键词:
非线性递推关系;  周期解;  生成元;  转化
Keywords:
nonlinear recurrence relation;  periodic solution;  generator;  translation
分类号:
O156.4
文献标志码:
A
摘要:
研究了带有高斯取整函数的两个非线性三项递推关系φk-1+φk+1=[φk], φk-1+φk+φk+1=[φk], k∈Z的周期性,通过递推分析找到了两个递推关系的所有解的最小正周期,并证明了任何解的周期均为12.
Abstract:
Two discontinuous three term recurrence relations φk-1+φk+1=[φk], and φk-1+φk+φk+1=[φk], k∈Z involving the Gauss bracket function are studied. By recursion and analysis, we find the least periods of all their solutions and prove that any solution has the period 12.

参考文献/References:

[1] Chang Y C, Wang G Q, Cheng S S. Complete set of periodic solutions of a discontinuous recurrence equation[J]. J Difference Eq Appl, 2012,18:1133-1162.
[2] Chang Y C, Cheng S S. Complete periodic behaviours of real and complex bang bang dynamical systems[J]. J Differecne Eq Appl, to appear.
[3] Chang Y C, Cheng S S. Complete periodicity analysis for a discontinuous recurrence equation[J]. Int J Bifurcation Chaos, 2013,23(4):1-34.
[4] Chang Y C, Wang G Q. Generators for nonlinear three term recurrences involving the greatest integer function[J]. Applied Mathematics E-Notes, 2011,11:73-81.
[5] Groove E A, Ladas G. Periodicities in Nonlinear Difference Equations[M]. Chap-man and Hall/CRC, 2004.

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备注/Memo

收稿日期: 2013-12-15*通信作者: 郑穗生(1953—),男,博士生导师,教授,研究方向为离散动力系统.

更新日期/Last Update: 2014-03-20