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Walking Cautiously Into the Collatz Wilderness: Algorithmically, Number Theoretically, Randomly
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities (2006).

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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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     author = {Belaga, Edward G. and Mignotte, Maurice},
     title = {Walking {Cautiously} {Into} the {Collatz} {Wilderness:} {Algorithmically,} {Number} {Theoretically,} {Randomly}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities},
     year = {2006},
     doi = {10.46298/dmtcs.3512},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3512/}
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Belaga, Edward G.; Mignotte, Maurice. Walking Cautiously Into the Collatz Wilderness: Algorithmically, Number Theoretically, Randomly. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, DMTCS Proceedings vol. AG, Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities (2006). doi : 10.46298/dmtcs.3512. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3512/

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