On the nonexistence of nontrivial small cycles of the µ function in 3 x +1 conjecture
作者: Dengguo FengXiubin FanLiping DingZhangyi Wang
作者单位: 1State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences
2Institute of Software, Chinese Academy of Sciences
刊名: Journal of Systems Science and Complexity, 2012, Vol.25 (6), pp.1215-1222
来源数据库: Springer Journal
DOI: 10.1007/s11424-012-0280-5
关键词: Diophantine equationeventual periodperiodic point3 x +1 conjecture
英文摘要: Abstract(#br)This paper studies the property of the recursive sequences in the 3 x + 1 conjecture. The authors introduce the concept of µ function, with which the 3 x + 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 3 x + 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 ≤ l ≤ 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 ≤ 68, and in this paper, the authors prove that there is no nontrivial l -cycle for...
全文获取路径: Springer  (合作)
分享到:
来源刊物:
影响因子:0.263 (2012)

×
关键词翻译
关键词翻译
  • conjecture 推测
  • nontrivial 非平凡
  • nonexistence 不存在性
  • function 函数
  • small 小的