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}
}
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… 
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