# The 3n+l-Problem and Holomorphic Dynamics

```@article{Letherman1999The3A,
title={The 3n+l-Problem and Holomorphic Dynamics},
author={Simon Letherman and Dierk Schleicher and Reginald M. W. Wood},
journal={Exp. Math.},
year={1999},
volume={8},
pages={241-251}
}```
• Published 1999
• Mathematics
• Exp. Math.
The 3n+1-problem is the following iterative procedure on the positive integers: the integer n maps to n/2 or 3n+1, depending on whether n is even or odd. It is conjectured that every positive integer will be eventually periodic, and the cycle it falls onto is 1 4 2 1. We construct entire holomorphic functions that realize the same dynamics on the integers and for which all the integers are in the Fatou set. We show that no integer is in a Baker domain (domain at infinity). We conclude that any…
17 Citations
3 n + 1 Problem and its Dynamics
• Mathematics
• 2020
The subject of this paper is the well-known 3n+ 1 problem of elementary number theory. This problem concerns with the behaviour of the iteration of a function which takes odd integers n to 3n + 1,
Dynamique du problème 3x + 1 sur la droite réelle
• Mathematics
• 2014
The 3x + 1 problem is a difficult conjecture dealing with quite a simple algorithm on the positive integers. A possible approach is to go beyond the discrete nature of the problem, following M.
Representing the integers with powers of 2 and 3
It follows that if the Collatz conjecture is true, then any number can be represented as sums of positive powers of 2 and negative powers of 3.
A refinement of the 3x + 1 conjecture
We reformulate the \$3x+1\$ conjecture by restricting attention to numbers congruent to \$2\$ (mod \$3\$). This leads to an equivalent conjecture for positive integers that reveals new aspects of the
A Refinement of the \$3x+1\$ Problem
We reformulate the \$3x+1\$ conjecture by restricting attention to numbers congruent to \$2\$ (mod \$3\$). This leads to an equivalent conjecture for positive integers that reveals new aspects of the
The real 3x + 1 problem
In this work, we introduce another extension U of the 3n+1 function to the real line. We propose a conjecture about the U-trajectories that generalizes the famous 3n+1 (or Collatz) conjecture. We
Dynamique du probl\`eme \$3x+1\$ sur la droite r\'eelle
• Mathematics
• 2014
The 3x+1 problem is a difficult conjecture dealing with quite a simple algorithm on the positive integers. A possible approach is to go beyond the discrete nature of the problem, following M.
Analyzing the Collatz Conjecture Using the Mathematical Complete Induction Method
• Mathematics
Mathematics
• 2022
In this paper, we demonstrate the Collatz conjecture using the mathematical complete induction method. We show that this conjecture is satisfied for the first values of natural numbers, and in
Holomorphic Dynamical Systems
• Mathematics
• 2010
This chapter is a survey on local dynamics of holomorphic maps in one and several complex variables, discussing in particular normal forms and the structure of local stable sets in the non-hyperbolic