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Hamiltonian character of the motion of the zeros of a polynomial whose coefficients oscillate over time

F Calogero and J-P Françoise

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A Hamiltonian is explicitly exhibited, whose equations of motion yield the time evolution of the n zeros, , of a polynomial of degree n in z, , when its coefficients oscillate, , or evolve in some other Hamiltonian manner.


PACS

02.30.Jr Partial differential equations

02.30.Ik Integrable systems

MSC

70H15 Canonical and symplectic transformations

70H08 Nearly integrable Hamiltonian systems, KAM theory

35G05 General theory of linear higher-order PDE

Subjects

Mathematical physics

Dates

Issue 1 (7 January 1997)

Received 12 January 1996, in final form 6 September 1996



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