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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)
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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
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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