Daniel Reyes, Miguel A. RodrÃguez, Piergiulio Tempesta
Published 2024-07-16Version 1
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.
Comments: 19 pages, 1 figure
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