Walking Cautiously into the Collatz Wilderness : Algorithmically, Number-Theoretically, Randomly

Edward G. Belaga (1) , Maurice Mignotte (1)

1 IRMA - Institut de Recherche Mathématique Avancée

"We present here our results in four domains closely related to the Collatz problem and its generalizations: algorithmic decidability, Diophantine representation, cyclic structure of related discrete dynamical systems, and divergent properties of such systems. This article has been published in the ""Fourth Colloquium on Mathematics and Computer Science : Algorithms, Trees, Combinatorics ans Probabilities"" .- September 18-22, 2006 ; Institut Elie Cartan, Nancy, France"

Mots clés: "Collatz problem; discrete dynamical system; cyclic and divergent trajectories; insolubility"; Collatz problem; insolubility

Domaines: Théorie des nombres [math.NT]

Edward G. Belaga, Maurice Mignotte. Walking Cautiously into the Collatz Wilderness : Algorithmically, Number-Theoretically, Randomly. 2006. ⟨hal-00129726⟩