Collatz's "3x+1" problem and iterative maps on interval

Details Collatz's "3x+1" problem and iterative maps on interval Collatz's "3x+1" problem and iterative maps on interval

2006-08-29

arxiv.org/abs/math/0608708v2

Mathematics

Number Theory

15 pages,4 figures

Scientific paper

In this paper, we convert Collatz map into a simple conjugate iterative maps
defined in [0,1]. Such maps are more familiar to us and easier to deal with.
Some new features of this map are observed by this method. An interesting
heuristic proof is also presented. This research may provide a new venture to
crack the "3x+1" problem.

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