On Generalized Convergence in Collatz Systems

The Collatz Conjecture belongs to the generalized class of Dynamicalsystem δk + β, where δ = 3, β = 1.This paper establishes that such asystem converges to β as long as the conditions are suitable. A full de-scription of the Collatz system is given and formula derived for the reversenumber, synchronized elements(those with similar Collatz Sequence) andclosed forms that can help ease with the computation.One of the most important discoveries of this paper is that the CollatzSpace is bounded by 1 at the end and by an odd multiple of 3 on theother end. From this a proof of the elusive conjecture can then be derivedeasily