Stochastic Models for the 3x+1 and 5x+1 Problems
Alex V. Kontorovich, Jeffrey C. Lagarias
TL;DR
This paper develops and analyzes stochastic models to predict the long-term behavior of orbits in the 3x+1 and 5x+1 problems, providing heuristic conjectures for their dynamics.
Contribution
It introduces rigorously analyzable stochastic models that offer new heuristic insights into the behavior of 3x+1 and 5x+1 orbits.
Findings
Heuristic predictions for orbit behavior
Rigorous stochastic models for 3x+1 and 5x+1
Conjectures on long-term dynamics
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.
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Taxonomy
TopicsBenford’s Law and Fraud Detection · Computability, Logic, AI Algorithms