Multi-Hamiltonian property of a linear system with quadratic invariant

Kozlov, V.

doi:10.1090/spmj/1574

Multi-Hamiltonian property of a linear system with quadratic invariant
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by V. V. Kozlov
Translated by: S. Yu. Pilyugin

St. Petersburg Math. J. 30 (2019), 877-883

DOI: https://doi.org/10.1090/spmj/1574

Published electronically: July 26, 2019

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Abstract:

It is shown that a nondegenerate linear system that admits a nondegenerate quadratic from as a first integral can be represented in several different ways as a Hamiltonian system of differential equations; we present a “complete” family of the corresponding symplectic structures and Hamiltonians. We discuss possible generalizations of this result including the case of linear systems of differential equations with periodic coefficients.

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