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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).

Abstract

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 1421. 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.

Citation

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

Information

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

zbMATH: 1012.37028
MathSciNet: MR1724157

Subjects:
Primary: 37F10
Secondary: 11B83 , 37F50

Rights: Copyright © 1999 A K Peters, Ltd.

Vol.8 • No. 3 • 1999
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