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

Abstract

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.

68 pages, 9 figures, 4 tables

References in corpus (1)

• Benford's Law, Values of L-functions and the 3x+1 Problem

Cited by in corpus (2)

• Conservation of Singularities in Functional Equations Associated to Collatz-Type Dynamical Systems; or, Dreamcatchers for Hydra Maps
• The Collatz Conjecture & Non-Archimedean Spectral Theory -- Part I.5 -- How To Write The (Weak) Collatz Conjecture As A Contour Integral