A Frobenius-type theory for discrete systems

2024/07/16 by D.F. Reyes, Reyes, Daniel, Miguel A. Rodrı́guez +3 · 1 citation
Computer Science · Mathematics · #37J70 #39A05 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #FOS: Physical sciences #Mathematical Physics (math-ph) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2407.11602

openalex publication_date 2024/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop an approach analogous to classical Frobenius theory for the analysis of singularities of ODEs in the case of discrete dynamical systems. Our methodology is based on the Roman-Rota theory of finite operators and relies crucially on the idea of preserving the Leibniz rule on a lattice of points by means of the notion of Rota algebras. The relevant cases of the Bessel, Hermite and Airy equations are discussed.

Cited by

• Laurent Sequences, Extended Rota Algebras and Categorical Discretization of Dynamical Systems

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