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Mat. Sb. (N.S.), 1983, Volume 121(163), Number 3(7), Pages 297–309 (Mi msb2194)  

This article is cited in 7 scientific papers (total in 7 papers)

On invariant measures for classical dynamical systems with infinite-dimensional phase space

A. A. Arsen'ev


Abstract: The Kubo–Martin–Schwinger state is constructed for a Hamiltonian dynamical system whose phase space is Hilbert space, with Hamiltonian representable as the sum of two terms: the square of the norm and a function that is smooth on the completion of the original space in the nuclear norm.
Bibliography: 5 titles.

Full text: PDF file (568 kB)
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English version:
Mathematics of the USSR-Sbornik, 1984, 49:2, 291–303

Bibliographic databases:

UDC: 517.946.9+531.19
MSC: Primary 28C10, 58F05; Secondary 47B10, 58D20, 70H05, 70H15
Received: 08.09.1981

Citation: A. A. Arsen'ev, “On invariant measures for classical dynamical systems with infinite-dimensional phase space”, Mat. Sb. (N.S.), 121(163):3(7) (1983), 297–309; Math. USSR-Sb., 49:2 (1984), 291–303

Citation in format AMSBIB
\Bibitem{Ars83}
\by A.~A.~Arsen'ev
\paper On invariant measures for classical dynamical systems with infinite-dimensional phase space
\jour Mat. Sb. (N.S.)
\yr 1983
\vol 121(163)
\issue 3(7)
\pages 297--309
\mathnet{http://mi.mathnet.ru/msb2194}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=707998}
\zmath{https://zbmath.org/?q=an:0542.58007}
\transl
\jour Math. USSR-Sb.
\yr 1984
\vol 49
\issue 2
\pages 291--303
\crossref{https://doi.org/10.1070/SM1984v049n02ABEH002711}


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    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. N. V. Peskov, “On a Kubo–Martin–Schwinger state of the sine-Gordon system”, Theoret. and Math. Phys., 64:1 (1985), 666–672  mathnet  crossref  mathscinet  zmath  isi
    2. I. D. Chueshov, “Equilibrium statistical solutions for dynamical systems with an infinite number of degrees of freedom”, Math. USSR-Sb., 58:2 (1987), 397–406  mathnet  crossref  mathscinet  zmath
    3. I. D. Chueshov, “Structure of the equilibrium states of a class of dynamical systems associated with Lie–Poisson brackets”, Theoret. and Math. Phys., 75:3 (1988), 640–644  mathnet  crossref  mathscinet  zmath  isi
    4. Zhidkov P., “An Invariant Measure for a Nonlinear-Wave Equation”, Nonlinear Anal.-Theory Methods Appl., 22:3 (1994), 319–325  crossref  mathscinet  zmath  isi
    5. Zhidkov P., “On Invariant-Measures for Some Infinite-Dimensional Dynamical-Systems”, Ann. Inst. Henri Poincare-Phys. Theor., 62:3 (1995), 267–287  mathscinet  zmath  isi
    6. P. E. Zhidkov, “Invariant measures generated by higher conservation laws for the Korteweg–de Vries equations”, Sb. Math., 187:6 (1996), 803–822  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. Zhidkov, P, “Korteweg-de Vries and nonlinear Schroginger equations: Qualitative theory”, Korteweg-de Vries and Nonlinear Schroginger Equations: Qualitative Theory, 1756 (2001), 1  crossref  mathscinet  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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