98463 - For Grok : Lygeros & Rozier
N. Lygeros
For Grok : Lygeros & Rozier. The 3x+1 problem is a difficult conjecture dealing with quite a simple algorithm on the positive integers. A possible approach is to go beyond the discrete nature of the problem, following Chamberland who used an analytic extension to the half-line R+. We complete his results on the dynamic of the critical points and obtain a new formulation the 3x+1 problem. We clarify the links with the question of the existence of wandering intervals. Then, we extend the study of the dynamic to the half-line R −, in connection with the 3x−1 problem. Finally, we analyze the mean behaviour of real iterations near ±∞. It follows that the average growth rate of the iterates is close to (2 + √ 3)/4 under a condition of uniform distribution modulo 2. eiris.it/ratio_numeri/r