On invariant measures for some infinite-dimensional dynamical systems
Zhidkov, P. E.
Annales de l'I.H.P. Physique théorique, Tome 63 (1995), p. 267-287 / Harvested from Numdam
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@article{AIHPA_1995__62_3_267_0,
     author = {Zhidkov, P. E.},
     title = {On invariant measures for some infinite-dimensional dynamical systems},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {63},
     year = {1995},
     pages = {267-287},
     mrnumber = {1335059},
     zbl = {0826.35118},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1995__62_3_267_0}
}

Zhidkov, P. E. On invariant measures for some infinite-dimensional dynamical systems. Annales de l'I.H.P. Physique théorique, Tome 63 (1995) pp. 267-287. http://gdmltest.u-ga.fr/item/AIHPA_1995__62_3_267_0/

[1] L. Friedlander, An Invariant Measure for the Equation utt - uxx + u3 = 0, Commun Math. Phys., Vol. 98, 1985, pp. 1-16. | MR 785258 | Zbl 0576.35082

[2] G. Casati, I. Guarneri and F. Valz-Griz, Preliminaries to the Ergodic Theory of Infinite-Dimensional Systems: A model of Radiant Cavity, J. Statist. Phys., Vol. 30, 1983, pp. 195-218. | MR 710740

[3] P.E. Zhidkov, On an Invariant Measure for a Nonlinear Schrödinger Equation, Soviet Math. Dokl., Vol. 317, 1991, pp. 543-546. | MR 1121337 | Zbl 0806.35168

[4] P.E. Zhidkov, A Remark on the Invariant Measure for the Nonlinear Schrödinger Equation, Differential'nye Uravneniya (in Russian) (to appear). | MR 1121337

[5] P.E. Zhidkov, An Invariant Measure for a Nonlinear Wave Equation, J. Nonlinear Anal.: Theory, Meth. Appl., Vol. 22, 1994, pp. 319-325. | MR 1264088 | Zbl 0803.35098

[6] J.L. Lebowitz, H.A. Rose and E.R. Speer, Statistical Mechanics of the Nonlinear Schrödinger Equation, J. Statist. Phys., Vol. 50, 1988, pp. 657-687. | MR 939505 | Zbl 01397625

[7] A.A. Arsen'Ev, On Invariant Measures for Classical Dynamical Systems with an Infinite-Dimensional Phase Space, Math. USSR Sbornik., Vol. 121, 1983, pp. 297-309 (in Russian). | MR 707998 | Zbl 0542.58007

[8] I.D. Chueshov, Equilibrium Statistical Solutions for Dynamical Systems with an Infinite Number of Degrees of a Freedom, Math. USSR Sbornik, Vol. 58, 1987, pp. 397-406. | Zbl 0632.60108

[9] I.D. Chueshov, On the Structure of Equilibrium States for a Class of Dynamical Systems Connected with Lee-Poisson Brackets, Theoret. Mat. Fiz., Vol. 75, 1988, pp. 445-450 (in Russian). | MR 959727 | Zbl 0659.58011

[10] N.V. Peskov, The KMS State of a sin-Gordon System, Theoret. Mat. Fiz., Vol. 64, 1985, pp. 32-40 (in Russian). | MR 815095 | Zbl 0591.35072

[11] V.G. Makhankov, Dynamics of Classical Solitons (in Non-Integrable Systems), Phys. Reports, Vol. 35C, 1978, pp. 1-128. | MR 481361

[12] R.K. Dodd, J.C. Eilbeck, J.D. Gibbon and H.C. Morris, Solitons and Nonlinear Wave Equations, Acad. Press, London, 1984. | MR 696935 | Zbl 0496.35001

[13] M. Grillakis, J. Shatah and W. Strauss, Stability Theory of Solitary Waves in the Presence of Symmetry, 1, J. Funct. Anal., Vol. 74, 1987, pp. 160-197. | MR 901236 | Zbl 0656.35122

[14] Yu.L. Daletskii and S.V. Fomin, Measures and Differential Equations in Infinite-Dimensional Spaces, Nauka, Moscow, 1983 (in Russian). | MR 720545

[15] A.V. Skorokhod, Integration in Hilbert Space, Nauka, Moscow, 1975 (in Russian).

[16] H.-H. Kuo, Gaussian Measures in Banach Spaces, Lect. Notes in Math., Vol. 463, 1975. | MR 461643 | Zbl 0306.28010

[17] V. Nemytskii and V. Stepanov, Qualitative Theory of Differential Equations, Moscow- Leningrad, 1949 (in Russian).

[18] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 2, Fourier Analysis, Self-Adjointness, Acad. Press, New York, 1975. | Zbl 0308.47002

[19] T. Kato, On Nonlinear Schrödinger Equations, Ann. Inst. Henri-Poincaré, Phys. Theor., Vol. 46, 1987, pp. 113-129. | Numdam | MR 877998 | Zbl 0632.35038

[20] D. Michalache, R.G. Nazmitdinov and V.K. Fedyanin, Nonlinear Optical Waves in Layered Structures, Prepr. JINR, 1988, E17-88-66, Dubna.

[21] P.E. Zhidkov, On the Cauchy Problem for a Generalized Korteweg-de Vries Equation with a Periodic Initial Data, Differential'nye Uravneniya, Vol. 26, 1990, pp. 823-829 (in Russian). | MR 1061251 | Zbl 0734.35109

[22] H. Mc Kean and K. Vaninsky, Existence of Flow and Invariance of Canonical Measure for Focussing and de-Focussing Cubic Schrödinger Equation on the Circle, Commun Math. Phys. (to appear).