On the Darboux-Halphen system: Jacobi vs Lie
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, R) which is non-integrable in Lie's terminology.
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