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…
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