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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 
 

 

Multi-Hamiltonian property of a linear system with quadratic invariant


Author: V. V. Kozlov
Translated by: S. Yu. Pilyugin
Original publication: Algebra i Analiz, tom 30 (2018), nomer 5.
Journal: St. Petersburg Math. J. 30 (2019), 877-883
MSC (2010): Primary 37K05
DOI: https://doi.org/10.1090/spmj/1574
Published electronically: July 26, 2019
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

V. V. Kozlov
Affiliation: 119991, Steklov Mathematical Institute, ul. Gubkina, 8 Moscow, Russia
Email: kozlov@pran.ru, vvkozlov@mi.ras.ru

DOI: https://doi.org/10.1090/spmj/1574
Keywords: Multi-Hamiltonian systems, compatible symplestic structures, symplectic map, quadratic invarnant, Cayley transform
Received by editor(s): January 23, 2018
Published electronically: July 26, 2019
Additional Notes: This research was supported by the Russian Science Foundation (project no. 14-50-00005)
Article copyright: © Copyright 2019 American Mathematical Society