@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},
pages = {267--287},
year = {1995},
publisher = {Gauthier-Villars},
volume = {62},
number = {3},
mrnumber = {1335059},
zbl = {0826.35118},
language = {en},
url = {https://www.numdam.org/item/AIHPA_1995__62_3_267_0/}
}
TY - JOUR AU - Zhidkov, P. E. TI - On invariant measures for some infinite-dimensional dynamical systems JO - Annales de l'I.H.P. Physique théorique PY - 1995 SP - 267 EP - 287 VL - 62 IS - 3 PB - Gauthier-Villars UR - https://www.numdam.org/item/AIHPA_1995__62_3_267_0/ LA - en ID - AIHPA_1995__62_3_267_0 ER -
Zhidkov, P. E. On invariant measures for some infinite-dimensional dynamical systems. Annales de l'I.H.P. Physique théorique, Tome 62 (1995) no. 3, pp. 267-287. https://www.numdam.org/item/AIHPA_1995__62_3_267_0/
[1] , An Invariant Measure for the Equation utt - uxx + u3 = 0, Commun Math. Phys., Vol. 98, 1985, pp. 1-16. | Zbl | MR
[2] , and , Preliminaries to the Ergodic Theory of Infinite-Dimensional Systems: A model of Radiant Cavity, J. Statist. Phys., Vol. 30, 1983, pp. 195-218. | MR
[3] , On an Invariant Measure for a Nonlinear Schrödinger Equation, Soviet Math. Dokl., Vol. 317, 1991, pp. 543-546. | Zbl | MR
[4] , A Remark on the Invariant Measure for the Nonlinear Schrödinger Equation, Differential'nye Uravneniya (in Russian) (to appear). | MR
[5] , An Invariant Measure for a Nonlinear Wave Equation, J. Nonlinear Anal.: Theory, Meth. Appl., Vol. 22, 1994, pp. 319-325. | Zbl | MR
[6] , and , Statistical Mechanics of the Nonlinear Schrödinger Equation, J. Statist. Phys., Vol. 50, 1988, pp. 657-687. | Zbl | MR
[7] , On Invariant Measures for Classical Dynamical Systems with an Infinite-Dimensional Phase Space, Math. USSR Sbornik., Vol. 121, 1983, pp. 297-309 (in Russian). | Zbl | MR
[8] , 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
[9] , 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). | Zbl | MR
[10] , The KMS State of a sin-Gordon System, Theoret. Mat. Fiz., Vol. 64, 1985, pp. 32-40 (in Russian). | Zbl | MR
[11] , Dynamics of Classical Solitons (in Non-Integrable Systems), Phys. Reports, Vol. 35C, 1978, pp. 1-128. | MR
[12] , , and , Solitons and Nonlinear Wave Equations, Acad. Press, London, 1984. | Zbl | MR
[13] , and , Stability Theory of Solitary Waves in the Presence of Symmetry, 1, J. Funct. Anal., Vol. 74, 1987, pp. 160-197. | Zbl | MR
[14] and , Measures and Differential Equations in Infinite-Dimensional Spaces, Nauka, Moscow, 1983 (in Russian). | MR
[15] , Integration in Hilbert Space, Nauka, Moscow, 1975 (in Russian).
[16] , Gaussian Measures in Banach Spaces, Lect. Notes in Math., Vol. 463, 1975. | Zbl | MR
[17] and , Qualitative Theory of Differential Equations, Moscow- Leningrad, 1949 (in Russian).
[18] and , Methods of Modern Mathematical Physics, Vol. 2, Fourier Analysis, Self-Adjointness, Acad. Press, New York, 1975. | Zbl
[19] , On Nonlinear Schrödinger Equations, Ann. Inst. Henri-Poincaré, Phys. Theor., Vol. 46, 1987, pp. 113-129. | Zbl | MR | Numdam
[20] , and , Nonlinear Optical Waves in Layered Structures, Prepr. JINR, 1988, E17-88-66, Dubna.
[21] , 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). | Zbl | MR
[22] and , Existence of Flow and Invariance of Canonical Measure for Focussing and de-Focussing Cubic Schrödinger Equation on the Circle, Commun Math. Phys. (to appear).





