Stochastic Models for the 3x+1 and 5x+1 Problems

Alex V. Kontorovich; Jeffrey C. Lagarias

Stochastic Models for the 3x+1 and 5x+1 Problems

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arxiv 0910.1944 v1 pith:DUYTDZ5Z submitted 2009-10-11 math.NT

Alex V. Kontorovich , Jeffrey C. Lagarias This is my paper · ORCID

classification math.NT

keywords modelsorbitsstochasticbehaviorproblemanalyzablecomparisonconjectures

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This paper discusses stochastic models for predicting the long-time behavior of the trajectories of orbits of the 3x+1 problem and, for comparison, the 5x+1 problem. The stochastic models are rigorously analyzable, and yield heuristic predictions (conjectures) for the behavior of 3x+1 orbits and 5x+1 orbits.

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$\left(p,q\right)$-adic Analysis and the Collatz Conjecture
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For a wide class of Collatz-type maps, the paper characterizes nonzero periodic points as integer values of a (p,q)-adic interpolation function and recasts the periodic-point question as a translate-density question, ...

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