Title: on the nonexistence of nontrivial small cycles of the μ function in 3x+1 conjecture

Author: Feng Dengguo
; Fan Xiubin
; Ding Liping
; Wang Zhangyi
Keyword: Systems science
Source: Journal of Systems Science and Complexity
Issued Date: 2012
Volume: 25, Issue: 6, Pages: 1215-1222 Indexed Type: EI
Department: (1) State Key Laboratory of Information Security Institute of Software Chinese Academy of Sciences Beijing 100190 China; (2) Institute of Software Chinese Academy of Sciences Beijing 100190 China
Abstract: This paper studies the property of the recursive sequences in the 3x + 1 conjecture. The authors introduce the concept of μ function, with which the 3x + 1 conjecture can be transformed into two other conjectures: one is eventually periodic conjecture of the μ function and the other is periodic point conjecture. The authors prove that the 3x + 1 conjecture is equivalent to the two conjectures above. In 2007, J. L. Simons proved the non-existence of nontrivial 2-cycle for the T function. In this paper, the authors prove that the μ function has no l-periodic points for 2 &le l &le 12. In 2005, J. L. Simons and B. M. M de Weger proved that there is no nontrivial l-cycle for the T function for l &le 68, and in this paper, the authors prove that there is no nontrivial l-cycle for the μ function for 2 &le l &le 102. © 2012 Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg.
English Abstract: This paper studies the property of the recursive sequences in the 3x + 1 conjecture. The authors introduce the concept of μ function, with which the 3x + 1 conjecture can be transformed into two other conjectures: one is eventually periodic conjecture of the μ function and the other is periodic point conjecture. The authors prove that the 3x + 1 conjecture is equivalent to the two conjectures above. In 2007, J. L. Simons proved the non-existence of nontrivial 2-cycle for the T function. In this paper, the authors prove that the μ function has no l-periodic points for 2 &le l &le 12. In 2005, J. L. Simons and B. M. M de Weger proved that there is no nontrivial l-cycle for the T function for l &le 68, and in this paper, the authors prove that there is no nontrivial l-cycle for the μ function for 2 &le l &le 102. © 2012 Institute of Systems Science, Academy of Mathematics and Systems Science, CAS and Springer-Verlag Berlin Heidelberg.
Language: 英语
Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/15429
Appears in Collections: 软件所图书馆_期刊论文

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Recommended Citation:
Feng Dengguo,Fan Xiubin,Ding Liping,et al. on the nonexistence of nontrivial small cycles of the μ function in 3x+1 conjecture[J]. Journal of Systems Science and Complexity,2012-01-01,25(6):1215-1222.