Matematicheskie Zametki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
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


Mat. Zametki, 2020, Volume 108, Issue 3, Pages 360–365 (Mi mz12817)  

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

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.


DOI: https://doi.org/10.4213/mzm12817

Full text: PDF file (405 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Mathematical Notes, 2020, 108:3, 339–343

Bibliographic databases:

UDC: 517.91
Received: 24.03.2020

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/mz12817}
\crossref{https://doi.org/10.4213/mzm12817}
\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{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000584617700003}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85093836615}


Linking options:
  • http://mi.mathnet.ru/eng/mz12817
  • https://doi.org/10.4213/mzm12817
  • http://mi.mathnet.ru/eng/mz/v108/i3/p360

    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

    This publication is cited in the following 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  isi  elib
    2. V. I. Bogachev, “On Sequential Properties of Spaces of Measures”, Math. Notes, 110:3 (2021), 449–453  mathnet  crossref  crossref  isi
  • Математические заметки Mathematical Notes
    Number of views:
    This page:213
    References:9
    First page:25

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021