On the 3x+1 conjecture

Abstract

In this paper, we discuss the well known 3x+1 conjecture in form of the accelerated Collatz function T defined on the positive odd integers. We present a sequence of quotient spaces and an invertible map that are intrinsically related to the behavior of T. This approach allows to express the 3x+1 conjecture in form of equivalent problems, which might be more accessible than the original conjecture.

11 pages. This is a slightly revised version of the original manuscript: an outline of our approach and its current shortcomings has been added (see Remarks 2.1 and 2.2)