on the nonexistence of nontrivial small cycles of the μ function in 3x+1 conjecture
文献类型：期刊论文
| 作者 | Feng Dengguo ; Fan Xiubin ; Ding Liping ; Wang Zhangyi |
| 刊名 | Journal of Systems Science and Complexity
 |
| 出版日期 | 2012 |
| 卷号 | 25期号:6页码:1215-1222 |
| 关键词 | Systems science |
| ISSN号 | 1009-6124 |
| 中文摘要 | 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. |
| 英文摘要 | 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. |
| 收录类别 | EI |
| 语种 | 英语 |
| 公开日期 | 2013-09-17 |
| 源URL | [http://ir.iscas.ac.cn/handle/311060/15429]  |
| 专题 | 软件研究所_软件所图书馆_期刊论文 |
| 推荐引用方式 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. |
入库方式： OAI收割
来源：软件研究所
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