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 Mat. Sb. (N.S.), 1986, Volume 130(172), Number 3(7), Pages 394–403 (Mi msb1883)

Equilibrium statistical solutions for dynamical systems with an infinite number of degrees of freedom

I. D. Chueshov

Abstract: In the case of formally Hamiltonian systems a certain class of statistical solutions which it is natural to call equilibrium solutions is singled out. The properties of these solutions are studied. If the system is sufficiently regular, then each equilibrium solution satisfies the Kubo–Martin–Schwinger condition in the classical form.
Bibliography: 15 titles.

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English version:
Mathematics of the USSR-Sbornik, 1987, 58:2, 397–406

Bibliographic databases:

UDC: 517.9+531.19
MSC: Primary 34C35; Secondary 47A70, 58F05, 70H99

Citation: I. D. Chueshov, “Equilibrium statistical solutions for dynamical systems with an infinite number of degrees of freedom”, Mat. Sb. (N.S.), 130(172):3(7) (1986), 394–403; Math. USSR-Sb., 58:2 (1987), 397–406

Citation in format AMSBIB
\Bibitem{Chu86} \by I.~D.~Chueshov \paper Equilibrium statistical solutions for dynamical systems with an infinite number of degrees of freedom \jour Mat. Sb. (N.S.) \yr 1986 \vol 130(172) \issue 3(7) \pages 394--403 \mathnet{http://mi.mathnet.ru/msb1883} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=865768} \zmath{https://zbmath.org/?q=an:0632.60108|0624.60115} \transl \jour Math. USSR-Sb. \yr 1987 \vol 58 \issue 2 \pages 397--406 \crossref{https://doi.org/10.1070/SM1987v058n02ABEH003110} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. 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
2. P.E. Zhidkov, “An invariant measure for a nonlinear wave equation”, Nonlinear Analysis: Theory, Methods & Applications, 22:3 (1994), 319
3. Zhidkov P., “On Invariant-Measures for Some Infinite-Dimensional Dynamical-Systems”, Ann. Inst. Henri Poincare-Phys. Theor., 62:3 (1995), 267–287
4. P. E. Zhidkov, “Invariant measures generated by higher conservation laws for the Korteweg–de Vries equations”, Sb. Math., 187:6 (1996), 803–822
5. Zhidkov, P, “Korteweg-de Vries and nonlinear Schroginger equations: Qualitative theory”, Korteweg-de Vries and Nonlinear Schroginger Equations: Qualitative Theory, 1756 (2001), 1
6. Hakima Bessaih, Benedetta Ferrario, “Invariant Gibbs measures of the energy for shell models of turbulence: the inviscid and viscous cases”, Nonlinearity, 25:4 (2012), 1075
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