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The complex geometry of an integrable system. (English) Zbl 1110.70022

Using the ideas by M. Adler and P. van Moerbeke [Invent. Math. 67, 297–331 (1982; Zbl 0539.58012)], the author studies a special algebraic completely integrable system. He shows that the intersection of levels of integrals completes into an abelian surface (a two-dimensional complex algebraic torus) of polarization (2,8), and that the flow of the system can be linearized on it.

MSC:

70H06 Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics
70G55 Algebraic geometry methods for problems in mechanics
14H70 Relationships between algebraic curves and integrable systems

Citations:

Zbl 0539.58012
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