Galois differential algebras and categorical discretization of dynamical\n systems

2014/07/23 by Piergiulio Tempesta, Tempesta, Piergiulio
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Analysis Techniques #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1407.6176

openalex publication_date 2014/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A categorical theory for the discretization of a large class of dynamical\nsystems with variable coefficients is proposed. It is based on the existence of\ncovariant functors between the Rota category of Galois differential algebras\nand suitable categories of abstract dynamical systems. The integrable maps\nobtained share with their continuous counterparts a large class of solutions\nand, in the linear case, the Picard-Vessiot group.\n

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