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arXiv · 1610.02545

Analogues of the $3x + 1$ Problem in Polynomial Rings of Characteristic 2

Daniel Nichols
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Abstract

The Collatz conjecture (also known as the $3x+1$ problem) concerns the behavior of the discrete dynamical system on the positive integers defined by iteration of the so-called $3x + 1$ function. We investigate analogous dynamical systems in rings of functions of algebraic curves over $\mathbb{F}_2$ . We prove in this setting a generalized analogue of a theorem of Terras concerning the asymptotic distribution of stopping times. We also present experimental data on the behavior of these dynamical systems.

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Daniel Nichols. 2016-10-08. Analogues of the $3x + 1$ Problem in Polynomial Rings of Characteristic 2. https://doi.org/10.1080/10586458.2016.1227734

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