The 3x+1 Periodicity Conjeture in $\mathbb{R}$

Josefina López, Peter Stoll

The $3x+1$ map $T$ is defined on the $2$-adic integers ${\mathbb{Z}}_2$ by $T(x)=x/2$ for even $x$ and $T(x)=(3x+1)/2$ for odd $x$. It is still unproved that under iteration of $T$ t…