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Tr. 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:

Document Type: Article
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, Tr. Mat. Inst. Steklova, 268, MAIK Nauka/Interperiodica, Moscow, 2010, 155–167; Proc. Steklov Inst. Math., 268 (2010), 148–160

Citation in format AMSBIB
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\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 Tr. Mat. Inst. Steklova
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\vol 268
\pages 155--167
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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    Citing articles on Google Scholar: Russian citations, English citations
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    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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    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  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. M. N. Davletshin, “Hill’s formula for $g$-periodic trajectories of Lagrangian systems”, Trans. Moscow Math. Soc., 74 (2013), 65–96  mathnet  crossref  mathscinet  zmath  elib
    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  mathnet  crossref  crossref  mathscinet  isi  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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