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arXiv · 1506.07622

A Dual-Radix Modular Division Algorithm for Computing Periodic Orbits within Syracuse Dynamical Systems

Andrey Rukhin
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Abstract

This article analyzes the periodic orbits of Syracuse dynamical systems in a novel algebraic setting: the commutative ring of graded $n$-adic integers. Within this context, this article introduces a dual-radix modular division algorithm for computing the graded canonical expansions and graded quotients for a certain class of rational expressions that arise from periodic orbits within these dynamical systems. This division algorithm yields two novel methods for testing the integrality of the B\"{o}hm-Sontacchi numbers.

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Andrey Rukhin. 2015-06-25. A Dual-Radix Modular Division Algorithm for Computing Periodic Orbits within Syracuse Dynamical Systems. https://doi.org/10.13140/rg.2.2.18652.85128

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