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Neumann system and hyperelliptic \(\text{al}\) functions. (English) Zbl 1153.37428
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.

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
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