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

Edward G. Belaga 1 Maurice Mignotte 1
1 IRMA - Institut de Recherche Mathématique Avancée
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.
Keywords : discrete dynamical systems Collatz and Conway transforms or Collatz problem 3n+1 pseudo-rundom walks Diophantine approximations exponential Diophantine equations algorithmic decidability
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Communication dans un congrès
Chassaing, Philippe and others. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, pp.249-260, 2006, DMTCS Proceedings
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Edward G. Belaga, Maurice Mignotte. Walking Cautiously Into the Collatz Wilderness: Algorithmically, Number Theoretically, Randomly. Chassaing, Philippe and others. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, pp.249-260, 2006, DMTCS Proceedings. 〈hal-01184717〉

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