# Conservation of Singularities in Functional Equations Associated to Collatz-Type Dynamical Systems; or, Dreamcatchers for Hydra Maps

@article{Siegel2019ConservationOS, title={Conservation of Singularities in Functional Equations Associated to Collatz-Type Dynamical Systems; or, Dreamcatchers for Hydra Maps}, author={Maxwell C. Siegel}, journal={arXiv: General Mathematics}, year={2019} }

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 of linear operators on spaces of analytic functions. Rather than studying potential fixed points of such operators, we examine their effect on the singularities of functions. To that end, we introduce the notion of a "dreamcatcher", an object which encodes the location and "virtual residue" of the…

## 2 Citations

Fourier Analysis of the Parity-Vector Parameterization of the Generalized Collatz px+1 maps

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- 2020

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…

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

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- 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…

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