A Dual-Radix Modular Division Algorithm for Computing Periodic Orbits within Syracuse Dynamical Systems
Andrey Rukhin
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 Böhm-Sontacchi number… Show more
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