Ordinary differential systems in dimension three with affine Weyl group symmetry of types D₄⁽¹⁾,B₃⁽¹⁾,G₂⁽¹⁾,D₃⁽²⁾ and A₂⁽²⁾

2007/04/18 by Yusuke Sasano, Sasano, Yusuke
Mathematics · Physics and Astronomy · #32S65 #34M45 #34M55 #58F05 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Nonlinear Waves and Solitons #math.AG #msc:32S65 #msc:34M45 #msc:34M55 #msc:58F05

paper · pdf · doi:10.48550/arxiv.0704.2391

14 pages, 1 figure

openalex publication_date 2007/04/18 · arxiv created 2009/12/14 · arxiv updated 2010/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a four-parameter family of ordinary differential systems in dimension three with affine Weyl group symmetry of type D₄⁽¹⁾. By obtaining its first integral, we can reduce this system to the second-order non-linear ordinary differential equations of Painlevé type. We also study this system restricted its parameters. Each system can be obtained by connecting some invariant divisors in the system of type D₄⁽¹⁾. Each system admits affine Weyl group symmetry of types B₃⁽¹⁾,G₂⁽¹⁾,D₃⁽²⁾ and A₂⁽²⁾, respectively. These symmetries, holomorphy conditions and invariant divisors are new.

Citations

• Symmetries in the system of type D₄⁽¹⁾
• Sur les équations différentielles du second ordre et du premier degré dont l'intégrale générale est a points critiques fixes

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