A Frobenius-Type Theory for Discrete Systems

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Studies in Applied Mathematics Pub Date : 2025-03-26 DOI:10.1111/sapm.70037

Daniel Reyes, Miguel A. Rodríguez, Piergiulio Tempesta

引用次数: 0

Abstract

We develop an approach analogous to the 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.

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离散系统的frobenius型理论

我们开发了一种类似于经典弗罗贝尼斯理论的方法，用于分析离散动力系统中 ODE 的奇异性。我们的方法以有限算子的 Roman-Rota 理论为基础，主要依赖于通过 Rota 矩的概念在点阵上保留莱布尼兹规则的思想。本文讨论了贝塞尔方程、赫米特方程和艾里方程的相关情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Studies in Applied Mathematics 数学-应用数学

CiteScore

4.30

自引率

3.70%

发文量

审稿时长

>12 weeks

期刊介绍： Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.