Collatz's "3x+1" problem and iterative maps on interval
arXiv:math/0608708
Abstract
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.
15 pages,4 figures