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Matematicheskie Zametki, 2017, Volume 101, Issue 6, Pages 911–918
DOI: https://doi.org/10.4213/mzm11520 (Mi mzm11520) 		 
This article is cited in 12 scientific papers (total in 12 papers)

On the Hamiltonian Property of Linear Dynamical Systems in Hilbert Space

D. V. Trescheva, A. A. Shkalikovb

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
b Lomonosov Moscow State University
Full-text PDF (456 kB) Citations (12)
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DOI: https://doi.org/10.4213/mzm11520
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 $\ker B \subset \ker A^*$. For a bounded linear mapping $x\to \Omega x$ possessing a first integral, sufficient conditions for the preservation of the (possibly degenerate) Poisson bracket are obtained.
Keywords: Hamiltonian system, Poisson bracket, symplectic structure.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-03747
16-01-00706
The work of the first author was supported by the Russian Foundation for Basic Research under grant 15-01-03747. The work of the second author was supported by the Russian Foundation for Basic Research under grant 16-01-00706.
Received: 07.09.2016
English version:
Mathematical Notes, 2017, Volume 101, Issue 6, Pages 1033–1039
DOI: https://doi.org/10.1134/S0001434617050303
Bibliographic databases:
Document Type: Article
UDC: 517.946
Language: Russian
Citation: D. V. Treschev, A. A. Shkalikov, “On the Hamiltonian Property of Linear Dynamical Systems in Hilbert Space”, Mat. Zametki, 101:6 (2017), 911–918; Math. Notes, 101:6 (2017), 1033–1039
Citation in format AMSBIB
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    • This publication is cited in the following 12 articles:
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