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1999 The 3n+1-problem and holomorphic dynamics
Simon Letherman, Dierk Schleicher, Reg Wood
Experiment. Math. 8(3): 241-251 (1999).


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 $1\mapsto 4\mapsto 2\mapsto 1$. 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 integer that is not eventually periodic must be in a wandering domain.


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Simon Letherman. Dierk Schleicher. Reg Wood. "The 3n+1-problem and holomorphic dynamics." Experiment. Math. 8 (3) 241 - 251, 1999.


Published: 1999
First available in Project Euclid: 9 March 2003

zbMATH: 1012.37028
MathSciNet: MR1724157

Primary: 37F10
Secondary: 11B83 , 37F50

Rights: Copyright © 1999 A K Peters, Ltd.


Vol.8 • No. 3 • 1999
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