On the Darboux-Halphen system: Jacobi vs Lie
Exactly Solvable and Integrable Systems
2026-05-14 v1 Mathematical Physics
Dynamical Systems
math.MP
Abstract
Two constructions of the Darboux-Halphen system are discussed. In the Jacobi construction we start with multi-valued functions which are fixed as the first integrals. In the Lie construction we use single-valued representation of the simple algebra which is non-integrable in Lie's terminology.
Cite
@article{arxiv.2605.13463,
title = {On the Darboux-Halphen system: Jacobi vs Lie},
author = {A. V. Tsiganov},
journal= {arXiv preprint arXiv:2605.13463},
year = {2026}
}
Comments
12 pages, LaTeX with AMS fonts