On the 3x+1 conjecture
  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. 
Peter Hellekalek
math.NT math.DS