Matematicheskie Zametki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find




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

Matematicheskie Zametki, 2020, Volume 108, Issue 3, Pages 360–365
DOI: https://doi.org/10.4213/mzm12817 (Mi mzm12817) 		 
This article is cited in 2 scientific papers (total in 2 papers)

The Liouville Equation as a Hamiltonian System

V. V. Kozlov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Full-text PDF (453 kB) Citations (2)
References:
PDF
HTML
DOI: https://doi.org/10.4213/mzm12817
Abstract: Smooth dynamical systems on closed manifolds with invariant measure are considered. The evolution of the density of a nonstationary invariant measure is described by the well-known Liouville equation. For ergodic dynamical systems, the Liouville equation is expressed in Hamiltonian form. An infinite collection of quadratic invariants that are pairwise in involution with respect to the Poisson bracket generated by the Hamiltonian structure is indicated.
Keywords: Liouville equation, Hamiltonian systems, integrability.
Funding agency Grant number
Russian Science Foundation 19-71-30012
This research was supported by the Russian Science Foundation under grant 19-71-30012.
Received: 24.03.2020
English version:
Mathematical Notes, 2020, Volume 108, Issue 3, Pages 339–343
DOI: https://doi.org/10.1134/S0001434620090035
Bibliographic databases:
Document Type: Article
UDC: 517.91
Language: Russian
Citation: V. V. Kozlov, “The Liouville Equation as a Hamiltonian System”, Mat. Zametki, 108:3 (2020), 360–365; Math. Notes, 108:3 (2020), 339–343
Citation in format AMSBIB
\Bibitem{Koz20}
\by V.~V.~Kozlov
\paper The Liouville Equation as a Hamiltonian System
\jour Mat. Zametki
\yr 2020
\vol 108
\issue 3
\pages 360--365
\mathnet{http://mi.mathnet.ru/mzm12817}
\crossref{https://doi.org/10.4213/mzm12817}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4153668}
\elib{https://elibrary.ru/item.asp?id=45205430}
\transl
\jour Math. Notes
\yr 2020
\vol 108
\issue 3
\pages 339--343
\crossref{https://doi.org/10.1134/S0001434620090035}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000584617700003}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85093836615}
Linking options:
  • https://www.mathnet.ru/eng/mzm12817
  • https://doi.org/10.4213/mzm12817
  • https://www.mathnet.ru/eng/mzm/v108/i3/p360
    • This publication is cited in the following 2 articles:
    1. V. V. Kozlov, “Quantization of linear systems of differential equations with a quadratic invariant in a Hilbert space”, Russian Math. Surveys, 76:2 (2021), 357–359  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    2. V. I. Bogachev, “On Sequential Properties of Spaces of Measures”, Math. Notes, 110:3 (2021), 449–453  mathnet  crossref  crossref  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
    Statistics & downloads:
    Abstract page:497
    Full-text PDF :106
    References:62
    First page:32
     
      Contact us:
    math-net2025_04@mi-ras.ru     		 Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025