THE 3 x + 1 CONJUGACY MAP
نویسندگان
چکیده
Daniel J. Bernstein, Jeffrey C. Lagarias 19960215 Abstra t. The 3x+1 map T and the shift map S are de ned by T (x) = (3x+1)=2 for x odd, T (x) = x=2 for x even, while S(x) = (x 1)=2 for x odd, S(x) = x=2 for x even. The 3x + 1 onjuga y map on the 2-adi integers Z2 onjugates S to T , i.e., Æ S Æ 1 = T . The map mod 2n indu es a permutation n on Z=2nZ. We study the y le stru ture of n. In parti ular we show that it has order 2n 4 for n 6. We also ount 1y les of n for n up to 1000; the results suggest that has exa tly two odd xed points. The results generalize to the ax + b map, where ab is odd. 1. Introdu tion Canadian Journal of Mathemati s 48 (1996), 1154{1169.
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