Enviar artigo por via de e-mail On the Hamiltonian property of linear dynamical systems in Hilbert space
- Autores: Treshchev D.V.1, Shkalikov A.A.2
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Afiliações:
- Steklov Mathematical Institute of Russian Academy of Sciences
- Lomonosov Moscow State University
- Edição: Volume 101, Nº 5-6 (2017)
- Páginas: 1033-1039
- Seção: 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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Resumo
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.
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Sobre autores
D. Treshchev
Steklov Mathematical Institute of Russian Academy of Sciences
Autor responsável pela correspondência
Email: treschev@mi.ras.ru
Rússia, Moscow
A. Shkalikov
Lomonosov Moscow State University
Email: treschev@mi.ras.ru
Rússia, Moscow
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