Matsutani, Shigeki Neumann system and hyperelliptic \(\text{al}\) functions. (English) Zbl 1153.37428 Surv. Math. Appl. 3, 13-25 (2008). Summary: This article shows that the Neumann dynamical system is described well in terms of the Weierstrass hyperelliptic \(\text{al}\) functions. The descriptions are very primitive; their proofs are provided only by residual computations but don’t require any theta functions. Cited in 2 Documents MSC: 37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests 14H70 Relationships between algebraic curves and integrable systems 33E05 Elliptic functions and integrals Keywords:Neumann system; Weierstrass hyperelliptic functions PDFBibTeX XMLCite \textit{S. Matsutani}, Surv. Math. Appl. 3, 13--25 (2008; Zbl 1153.37428) Full Text: arXiv EuDML