Towards an algebro-geometric interpretation of the neumann system

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Abstract

Lax equations and constants of motion for C. Neumann's system of constrained harmonic oscillators are derived in a systematic wayfrom the Burchnall-Chaundy-Krichever theory of 2nd-order differential operators D2+q(t). The approach is based on a geometric step: to map the algebraic curve and linebundle associated with D2 + q(t) to a larger projective space by means of a suitable linear system. The image of D2 + q(t) is, roughly speaking, just the Lax operator for the Neumann system.

Original languageEnglish (US)
Pages (from-to)407-426
Number of pages20
JournalTohoku Mathematical Journal
Volume36
Issue number3
DOIs
StatePublished - Sep 1984

ASJC Scopus subject areas

  • Mathematics(all)

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