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 Trudy Mat. Inst. Steklova, 2010, Volume 268, Pages 155–167 (Mi tm2874)

This article is cited in 4 scientific papers (total in 4 papers)

Spectral properties of operators with polynomial invariants in real finite-dimensional spaces

V. V. Kozlov

Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

Abstract: We consider linear operators lying in the orthogonal group of a quadratic form and study those spectral properties of such operators that can be expressed in terms of the signature of this form. We show that in the typical case these transformations are symplectic. Some of the results can be extended to the general case when the operator admits a homogeneous form of degree $\ge3$.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2010, 268, 148–160

Bibliographic databases:

UDC: 517.984
Received in May 2009

Citation: V. V. Kozlov, “Spectral properties of operators with polynomial invariants in real finite-dimensional spaces”, Differential equations and topology. I, Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 268, MAIK Nauka/Interperiodica, Moscow, 2010, 155–167; Proc. Steklov Inst. Math., 268 (2010), 148–160

Citation in format AMSBIB
\Bibitem{Koz10} \by V.~V.~Kozlov \paper Spectral properties of operators with polynomial invariants in real finite-dimensional spaces \inbook Differential equations and topology.~I \bookinfo Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin \serial Trudy Mat. Inst. Steklova \yr 2010 \vol 268 \pages 155--167 \publ MAIK Nauka/Interperiodica \publaddr Moscow \mathnet{http://mi.mathnet.ru/tm2874} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2724341} \zmath{https://zbmath.org/?q=an:1209.47005} \elib{https://elibrary.ru/item.asp?id=13726643} \transl \jour Proc. Steklov Inst. Math. \yr 2010 \vol 268 \pages 148--160 \crossref{https://doi.org/10.1134/S0081543810010128} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000277345600012} \elib{https://elibrary.ru/item.asp?id=15324625} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77952283559} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. S. V. Bolotin, D. V. Treschev, “Hill's formula”, Russian Math. Surveys, 65:2 (2010), 191–257
2. Budochkina S.A., Savchin V.M., “On $B_u$-Hamiltonian equations in mechanics of infinite-dimensional systems”, Dokl. Math., 84:1 (2011), 525–526
3. M. N. Davletshin, “Hill’s formula for $g$-periodic trajectories of Lagrangian systems”, Trans. Moscow Math. Soc., 74 (2013), 65–96
4. D. V. Treschev, A. A. Shkalikov, “On the Hamiltonian Property of Linear Dynamical Systems in Hilbert Space”, Math. Notes, 101:6 (2017), 1033–1039
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