on the nonexistence of nontrivial small cycles of the &mu; function in 3x+1 conjecture

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	on the nonexistence of nontrivial small cycles of the μ function in 3x+1 conjecture
	Feng Dengguo; Fan Xiubin; Ding Liping; Wang Zhangyi
	2012
Source	Journal of Systems Science and Complexity
ISSN	1009-6124
Volume	25 Issue:6 Pages:1215-1222
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.; 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.
Indexed Type	EI
Keyword	Systems Science
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
Language	英语
Content Type	期刊论文
URI	http://ir.iscas.ac.cn/handle/311060/15429
Collection	中国科学院软件研究所
Recommended Citation GB/T 7714	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,2012,25(6):1215-1222.
APA	Feng Dengguo,Fan Xiubin,Ding Liping,&Wang Zhangyi.(2012).on the nonexistence of nontrivial small cycles of the μ function in 3x+1 conjecture.Journal of Systems Science and Complexity,25(6),1215-1222.
MLA	Feng Dengguo,et al."on the nonexistence of nontrivial small cycles of the μ function in 3x+1 conjecture".Journal of Systems Science and Complexity 25.6(2012):1215-1222.

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