On the Darboux-Halphen system: Jacobi vs Lie

2026/05/13 by A. V. Tsiganov · 1 voice · 1 citation
Mathematics · Physics and Astronomy · #math-ph #math.DS #nlin.SI

paper · pdf · doi:10.1016/j.geomphys.2026.105914

arxiv published 2026/05/13 · arxiv updated 2026/06/11

Abstract

Two constructions of the Darboux-Halphen system are discussed. In the Jacobi construction we start with transcendental functions which are fixed as the first integrals. In the Lie construction we use a single-valued representation of the simple Lie algebra sl(2,\mathbb R) which is non-integrable in Lie's terminology.

Citations

• On the Lie noncommutative integrability
• On a reduction of the generalized Darboux-Halphen system
• Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55)
• Vorlesungen über analytische Mechanik

Cited by

• On the Lie noncommutative integrability

Discussions

• A. V. Tsiganov: On the Darboux-Halphen system: Jacobi vs Lie https://arxiv.org/abs/2605.13463 https://arxiv.org/pdf/2605.13463 https://arxiv.org/html/2605.13463 [bsky, 0 points, 0 comments]

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