Equivalence of differential equations of order one

2013/03/20 by L. X. Chau Ngo, L. X. Châu Ngô, Ngo, L. X. Chau +8 · 1 citation
Computer Science · Mathematics · #34M15 #34M35 #34M55 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:34M15 #msc:34M35 #msc:34M55

paper · pdf · doi:10.48550/arxiv.1303.4960

19 pages

arxiv created 2013/03/20 · openalex publication_date 2013/03/20 · arxiv updated 2013/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The notions of equivalence and strict equivalence for order one differential equations are introduced. The more explicit notion of strict equivalence is applied to examples and questions concerning autonomous equations and equations having the Painleve property. The order one equation determines an algebraic curve. If this curve has genus zero or one, then it is difficult to verify strict equivalence. However, for higher genus strict equivalence can be tested by an algorithm sketched in the text. For autonomous equations, testing strict equivalence and the existence of algebraic solutions are shown to be algorithmic.

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• Strongly Normal Extensions and Algebraic Differential Equations

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