摘要
深入研究并分析切比雪夫序列的短周期现象,并通过数学证明,对于任意整数阶切比雪夫序列,在初值角度取有限小数时必会退化为短周期序列.首先,通过证明得到切比雪夫序列退化为短周期序列的等价条件;然后,利用分类讨论的思想证明任意整数阶切比雪夫序列在初值角度取整数时,必会退化为短周期序列;最后,通过数学归纳法将这一结论扩展到任意有限精度初值上,得出切比雪夫序列在初值精度有限时退化为周期序列.
The short-period problems of Chebyshev sequences had been researched, and aconclusion that Chebyshev sequences of random integer order will degenerateinto short-period sequences while Chebyshev sequences' initial value is afinite decimal had been proved. The equivalent conditions about Chebyshevsequences degenerating into short-period sequences had been shown first, andthen an integer order Chebyshev sequences whose initial value is integermust degenerate into short-period sequence has been proved. Finally, theinitial value conditions has been extended to finite decimal by usingmathematical induction method.
出处
《北京邮电大学学报》
EI
CAS
CSCD
北大核心
2010年第1期102-105,共4页
Journal of Beijing University of Posts and Telecommunications
基金
教育部高等学校博士学科点专项科研基金项目(200800131002)
国家自然科学基金项目(60977002)
国家高技术研究发展计划项目(2009AA01Z220
2007AA03Z447)
新世纪优秀人才计划项目(NECT-07-0111)
教育部留学归国人员教学科研经费建设项目
关键词
混沌序列
切比雪夫映射
短周期
ehoatic sequences
chebyshev map
short periods