Ring of flows of one-dimensional differential equations

2020/06/08 by Ronald Orozco López, López, Ronald Orozco
Mathematics · #11B83 #16W99 #34A34 #47H99 #Advanced Differential Equations and Dynamical Systems #Differential Equations and Numerical Methods #Dynamical Systems (math.DS) #FOS: Mathematics #Rings and Algebras (math.RA) #advanced mathematical theories #math.DS #math.RA #msc:11B83 #msc:16W99 #msc:34A34 #msc:47H99

paper · pdf · doi:10.48550/arxiv.2006.04749

22 pages

openalex publication_date 2020/06/08 · arxiv created 2021/03/29 · arxiv updated 2021/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, the ring of flows of autonomous differential equations of order one on integral domains is constructed. First, we build the autonomous ring \Opa(\hurw_R[[x]]) and then its structure is studied. Next, we build the ring of formal exponential generating series of the ring \Opa(\hurw_ R [[x]]) , where it is possible to find solutions of differential equations of order one when the vector field of the system can be decomposed in sum or product of functions.

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