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Walking Cautiously Into the Collatz Wilderness: Algorithmically, Number Theoretically, Randomly

Abstract : Building on theoretical insights and rich experimental data of our preprints, we present here new theoretical and experimental results in three interrelated approaches to the Collatz problem and its generalizations: \emphalgorithmic decidability, random behavior, and Diophantine representation of related discrete dynamical systems, and their \emphcyclic and divergent properties.
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Edward G. Belaga, Maurice Mignotte. Walking Cautiously Into the Collatz Wilderness: Algorithmically, Number Theoretically, Randomly. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. pp.249-260. ⟨hal-01184717⟩

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