# Syracuse Random Variables and the Periodic Points of Collatz-type maps

@article{Siegel2020SyracuseRV, title={Syracuse Random Variables and the Periodic Points of Collatz-type maps}, author={Maxwell C. Siegel}, journal={arXiv: General Mathematics}, year={2020} }

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 composition sequences of the maps $\frac{x}{2}$ and $\frac{px+1}{2}$ can be parameterized over the $2$-adic integers ($\mathbb{Z}_{2}$) leading to a continuous function from $\mathbb{Z}_2$ to $\mathbb{Z}_p$ which the author calls the numen of $H_{p}$, denoted $\chi_p$; the $p=3$ case turns out to be…

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