Projective Isomonodromy and Galois Groups

2010/02/10 by Claude Mitschi, Mitschi, Claude, Michael F. Singer +1
Mathematics · Physics and Astronomy · #12H05 #34M55 #34M56 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Waves and Solitons #math.CA #math.DS #msc:12H05 #msc:34M55 #msc:34M56

paper · pdf · doi:10.48550/arxiv.1002.2005

Version that will appear in the Proceedings of the American Mathematical Society

openalex publication_date 2010/02/10 · arxiv created 2012/06/01 · arxiv updated 2012/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we introduce the notion of projective isomonodromy, which is a special type of monodromy evolving deformation of linear differential equations, based on the example of the Darboux-Halphen equation. We give an algebraic condition for a paramaterized linear differential equation to be projectively isomonodromic, in terms of the derived group of its parameterized Picard-Vessiot group.

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