Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843 - 7265 (print)
 Volume 3 (2008), 13 -- 25

NEUMANN SYSTEM AND HYPERELLIPTIC AL FUNCTIONS

Shigeki Matsutani

Abstract. This article shows that the Neumann dynamical system is described well in terms of the Weierstrass hyperelliptic al functions. The descriptions are very primitive; their proofs are provided only by residual computations but don't require any theta functions.

2000 Mathematics Subject Classification: Primary 37K20, 14H81; Secondary 14K20, 14H70.
Keywords: Neumann system; Weierstrass hyperelliptic al functions.

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