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 Mat. Sb. (N.S.), 1981, Volume 115(157), Number 1(5), Pages 116–129 (Mi msb2376)

An example of a Kubo–Martin–Schwinger state for a nonlinear classical poisson system with infinite-dimensional phase space

A. A. Arsen'ev

Abstract: A “smoothed” nonlinear Klein–Gordon equation is regarded as the equation of evolution of a classical dynamical system with an infinite-dimensional phase space. It is proved that the wave operators are canonical transformations of this system that linearize it. It is shown that a Gaussian measure induces a Kubo–Martin–Schwinger state for the linear system, and that the preimage of this measure under the canonical transformation implemented by a wave operator is a Kubo–Martin–Schwinger state for the original nonlinear system.
Bibliography: 8 titles.

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English version:
Mathematics of the USSR-Sbornik, 1982, 43:1, 103–115

Bibliographic databases:

UDC: 517.9
MSC: Primary 58F05; Secondary 47L30, 58D25, 70G35, 76F99, 81C05

Citation: A. A. Arsen'ev, “An example of a Kubo–Martin–Schwinger state for a nonlinear classical poisson system with infinite-dimensional phase space”, Mat. Sb. (N.S.), 115(157):1(5) (1981), 116–129; Math. USSR-Sb., 43:1 (1982), 103–115

Citation in format AMSBIB
\Bibitem{Ars81} \by A.~A.~Arsen'ev \paper An example of a~Kubo--Martin--Schwinger state for a~nonlinear classical poisson system with infinite-dimensional phase space \jour Mat. Sb. (N.S.) \yr 1981 \vol 115(157) \issue 1(5) \pages 116--129 \mathnet{http://mi.mathnet.ru/msb2376} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=618590} \transl \jour Math. USSR-Sb. \yr 1982 \vol 43 \issue 1 \pages 103--115 \crossref{https://doi.org/10.1070/SM1982v043n01ABEH002433}