Edward G. Belaga ; Maurice Mignotte - Walking Cautiously Into the Collatz Wilderness: Algorithmically, Number Theoretically, Randomly

dmtcs:3512 - Discrete Mathematics & Theoretical Computer Science, January 1, 2006, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities - https://doi.org/10.46298/dmtcs.3512
Walking Cautiously Into the Collatz Wilderness: Algorithmically, Number Theoretically, Randomly

Authors: Edward G. Belaga 1; Maurice Mignotte 1

  • 1 Institut de Recherche Mathématique Avancée

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.

https://doi.org/10.46298/dmtcs.3512
Source: HAL:hal-01184717v1
Volume: DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities
Section: Proceedings
Published on: January 1, 2006
Imported on: May 10, 2017
Keywords: discrete dynamical systems, Collatz and Conway transforms, or Collatz problem,3n+1, pseudo-rundom walks, Diophantine approximations, exponential Diophantine equations, algorithmic decidability,[INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS],[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]

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