On invariant measures for some infinite-dimensional dynamical systems

P. E. Zhidkov

Annales de l'I.H.P. Physique théorique (1995)

  • Volume: 62, Issue: 3, page 267-287
  • ISSN: 0246-0211

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Zhidkov, P. E.. "On invariant measures for some infinite-dimensional dynamical systems." Annales de l'I.H.P. Physique théorique 62.3 (1995): 267-287. <http://eudml.org/doc/76676>.

@article{Zhidkov1995,
author = {Zhidkov, P. E.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {infinite-dimensional dynamical system; construction of an invariant measure; Poincaré recurrence; Fermi-Pasta-Ulam phenomenon},
language = {eng},
number = {3},
pages = {267-287},
publisher = {Gauthier-Villars},
title = {On invariant measures for some infinite-dimensional dynamical systems},
url = {http://eudml.org/doc/76676},
volume = {62},
year = {1995},
}

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
PB - Gauthier-Villars
VL - 62
IS - 3
SP - 267
EP - 287
LA - eng
KW - infinite-dimensional dynamical system; construction of an invariant measure; Poincaré recurrence; Fermi-Pasta-Ulam phenomenon
UR - http://eudml.org/doc/76676
ER -

References

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  1. [1] L. Friedlander, An Invariant Measure for the Equation utt - uxx + u3 = 0, Commun Math. Phys., Vol. 98, 1985, pp. 1-16. Zbl0576.35082MR785258
  2. [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. MR710740
  3. [3] P.E. Zhidkov, On an Invariant Measure for a Nonlinear Schrödinger Equation, Soviet Math. Dokl., Vol. 317, 1991, pp. 543-546. Zbl0806.35168MR1121337
  4. [4] P.E. Zhidkov, A Remark on the Invariant Measure for the Nonlinear Schrödinger Equation, Differential'nye Uravneniya (in Russian) (to appear). MR1121337
  5. [5] P.E. Zhidkov, An Invariant Measure for a Nonlinear Wave Equation, J. Nonlinear Anal.: Theory, Meth. Appl., Vol. 22, 1994, pp. 319-325. Zbl0803.35098MR1264088
  6. [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. Zbl1084.82506MR939505
  7. [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). Zbl0542.58007MR707998
  8. [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. Zbl0632.60108
  9. [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). Zbl0659.58011MR959727
  10. [10] N.V. Peskov, The KMS State of a sin-Gordon System, Theoret. Mat. Fiz., Vol. 64, 1985, pp. 32-40 (in Russian). Zbl0591.35072MR815095
  11. [11] V.G. Makhankov, Dynamics of Classical Solitons (in Non-Integrable Systems), Phys. Reports, Vol. 35C, 1978, pp. 1-128. MR481361
  12. [12] R.K. Dodd, J.C. Eilbeck, J.D. Gibbon and H.C. Morris, Solitons and Nonlinear Wave Equations, Acad. Press, London, 1984. Zbl0496.35001MR696935
  13. [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. Zbl0656.35122MR901236
  14. [14] Yu.L. Daletskii and S.V. Fomin, Measures and Differential Equations in Infinite–Dimensional Spaces, Nauka, Moscow, 1983 (in Russian). MR720545
  15. [15] A.V. Skorokhod, Integration in Hilbert Space, Nauka, Moscow, 1975 (in Russian). Zbl0355.62084
  16. [16] H.-H. Kuo, Gaussian Measures in Banach Spaces, Lect. Notes in Math., Vol. 463, 1975. Zbl0306.28010MR461643
  17. [17] V. Nemytskii and V. Stepanov, Qualitative Theory of Differential Equations, Moscow- Leningrad, 1949 (in Russian). Zbl0089.29502
  18. [18] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 2, Fourier Analysis, Self-Adjointness, Acad. Press, New York, 1975. Zbl0308.47002
  19. [19] T. Kato, On Nonlinear Schrödinger Equations, Ann. Inst. Henri-Poincaré, Phys. Theor., Vol. 46, 1987, pp. 113-129. Zbl0632.35038MR877998
  20. [20] D. Michalache, R.G. Nazmitdinov and V.K. Fedyanin, Nonlinear Optical Waves in Layered Structures, Prepr. JINR, 1988, E17-88-66, Dubna. 
  21. [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). Zbl0734.35109MR1061251
  22. [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). 

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