In 1995, Meinardus & Berg presented a reformulation of the Collatz Conjecture in terms of a functional equation in a single complex variable over the open unit disk. This paper generalizes that… Expand

Let p be an odd prime, and consider the map H_p which sends an integer x to either x/2 or (px+1)/2 depending on whether x is even or odd. The values at x=0 of arbitrary composition sequences of the… Expand

Let $p$ be an odd prime, and consider the map $H_{p}$ which sends an integer $x$ to either $\frac{x}{2}$ or $\frac{px+1}{2}$ depending on whether $x$ is even or odd. The values at $x=0$ of arbitrary… Expand

It is known that the Collatz Conjecture (and the study of similar maps, here called "Hydra maps") can be stated in terms of solution sets of functional equations; or, equivalently, the fixed points… Expand

Fix an integer ̺ ≥ 2. We consider maps H : Z → Z so that for any n ∈ Z, the value of H (n) is the image of one of ̺ distinct affine-linear maps, the choice of which is determined by the value of n… Expand