Email this article On the Hamiltonian property of linear dynamical systems in Hilbert space
- Authors: Treshchev D.V.1, Shkalikov A.A.2
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Affiliations:
- Steklov Mathematical Institute of Russian Academy of Sciences
- Lomonosov Moscow State University
- Issue: Vol 101, No 5-6 (2017)
- Pages: 1033-1039
- Section: Volume 101, Number 6, June, 2017
- URL: https://journals.rcsi.science/0001-4346/article/view/150064
- DOI: https://doi.org/10.1134/S0001434617050303
- ID: 150064
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Abstract
Conditions for the operator differential equation \(\dot x = Ax\) possessing a quadratic first integral (1/2)(Bx, x) to be Hamiltonian are obtained. In the finite-dimensional case, it suffices to require that ker B ⊂ ker A*. For a bounded linear mapping x → Ωx possessing a first integral, sufficient conditions for the preservation of the (possibly degenerate) Poisson bracket are obtained.
About the authors
D. V. Treshchev
Steklov Mathematical Institute of Russian Academy of Sciences
Author for correspondence.
Email: treschev@mi.ras.ru
Russian Federation, Moscow
A. A. Shkalikov
Lomonosov Moscow State University
Email: treschev@mi.ras.ru
Russian Federation, Moscow
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