Statistical (3x+1) -- problem

Details Statistical (3x+1) -- problem Statistical (3x+1) -- problem

2002-01-11

arxiv.org/abs/math/0201102v2

Mathematics

Dynamical Systems

15 pages, AMS tex. To be published in Comm. Pure Appl. Math. The second part of the paper is much shorter and significantly mo

Scientific paper

Take an odd number x >0. Then 3x+1 is even and one can find an integer k> 0
so that y= 3x+1/2^k is again odd. We get in this way the mapping T, Tx=y. The
paper contains two theorems describing statistical properties of T. The first
describes statistical properties of trajectories for large x. The second gives
some information about the probability distribution appearing in this problem.

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