RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Regul. Chaotic Dyn.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Regul. Chaotic Dyn., 2018, Volume 23, Issue 1, Pages 26–46 (Mi rcd306)  

Linear Hamiltonian Systems: Quadratic Integrals, Singular Subspaces and Stability

Valery V. Kozlov

Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: A chain of quadratic first integrals of general linear Hamiltonian systems that have not been represented in canonical form is found. Their involutiveness is established and the problem of their functional independence is studied. The key role in the study of a Hamiltonian system is played by an integral cone which is obtained by setting known quadratic first integrals equal to zero. A singular invariant isotropic subspace is shown to pass through each point of the integral cone, and its dimension is found. The maximal dimension of such subspaces estimates from above the degree of instability of the Hamiltonian system. The stability of typical Hamiltonian systems is shown to be equivalent to the degeneracy of the cone to an equilibrium point. General results are applied to the investigation of linear mechanical systems with gyroscopic forces and finite-dimensional quantum systems.

Keywords: Hamiltonian system, quadratic integrals, integral cones, degree of instability, quantum systems, Abelian integrals

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations 01
This work was carried out within the framework of the scientific program of the Presidium of the Russian Academy of Sciences 01 “Fundamental Mathematics and its Applications”.


DOI: https://doi.org/10.1134/S1560354718010033

References: PDF file   HTML file

Bibliographic databases:

Document Type: Article
MSC: 34A30
Received: 27.10.2017
Language: English

Citation: Valery V. Kozlov, “Linear Hamiltonian Systems: Quadratic Integrals, Singular Subspaces and Stability”, Regul. Chaotic Dyn., 23:1 (2018), 26–46

Citation in format AMSBIB
\Bibitem{Koz18}
\by Valery V. Kozlov
\paper Linear Hamiltonian Systems: Quadratic Integrals, Singular Subspaces and Stability
\jour Regul. Chaotic Dyn.
\yr 2018
\vol 23
\issue 1
\pages 26--46
\mathnet{http://mi.mathnet.ru/rcd306}
\crossref{https://doi.org/10.1134/S1560354718010033}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3759968}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000424267100003}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85041419489}


Linking options:
  • http://mi.mathnet.ru/eng/rcd306
  • http://mi.mathnet.ru/eng/rcd/v23/i1/p26

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Number of views:
    This page:73
    References:19

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2018