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Prog. Theor. Phys. Supplement No.64 (1978) pp. 339-345

[ Full Text PDF : FREE ACCESS (523K) ]

What Are the Measure Describing Turbulence?

David Ruelle

IHES, 91440 Bures-sur-Yvette

Abstract:

It is believed that the average properties of a dissipative dynamical system, in particular a turbulent flow, are described by a measure invariant under time evolution. We discuss here the problem of determining such measures (asymptotic measures).


URL : http://ptp.ipap.jp/link?PTPS/64/339/
DOI : 10.1143/PTPS.64.339

[ Full Text PDF : FREE ACCESS (523K) ] Citation:

References:

  1. R. Bowen, “Equilibrium States and the Ergoic Theory of Anosov Diffemorphisms”, Lecture Notes in Mathematics, No. 470 (Springer, Berlin, 1975).
  2. R. Bowen (to appear).
  3. R. Bowen and D. Ruelle, Inventiones Math. 29 (1975), 181.
  4. S. Katok, The Estimation from above for the Topological Entropy of a Diffeomorphism (to appear).
  5. Yu. I. Kifer, Doklady Akad. Nauk SSSR 216 (1974), 979 [English translation]; Sov. Math. Doklady 15 (1974), 918; Izv. Akad. Nauk SSSR: Ser. Mat. 38 (1974), 1091 [English translation]; Math. USSR Izvestija 8 (1974), 1083.
  6. E. N. Lorenz, J. Atmos. Sci. 20 (1963), 130.
  7. J. Mallet-Paret, J. Diff. Equations. 22 (1976), 331.
  8. D. Ruelle, Am. J. Math. 98 (1976), 619.
  9. D. Ruelle, Boll. Soc. Bras. Mat. 9 (1978), 83.
  10. D. Ruelle, “Sensitive Dependence on Initial Condition and Turbulent Behavior of Dynamical Systems”, Ann. N. Y. Acad. Sci. (to appear).
  11. D. Ruelle, “Ergodic Theory of Differentiable Dynamical Systems” (to appear).
  12. Ya. G. Sinai, Uspekhi Mat. Nauk 27 (1972), 21 [English translation]; Russian Math. Surveys 27 (1972), 21.
  13. S. Smale, Bull. Am. Math. Soc. 73 (1967), 747.

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 63 No. 6 (1980) pp. 1931-1944 :
    Statistical Dynamics of Chaotic Flows
    Hazime Mori and Hirokazu Fujisaka
  2. Progress of Theoretical Physics Vol. 64 No. 3 (1980) pp. 782-793 :
    Temporal Development of the Taylor Vortices in a Rotating Fluid. III
    Hideo Yahata
  3. Progress of Theoretical Physics Vol. 66 No. 4 (1981) pp. 1266-1283 :
    Time-Correlation Functions of One-Dimensional Transformations
    Hazime Mori, Byon-Chyol So and Tomoaki Ose
  4. Progress of Theoretical Physics Vol. 70 No. 5 (1983) pp. 1183-1196 :
    Intermittency and Relative Diffusion in Fully-Developed Turbulence
    Hazime Mori and Kiyofumi Takayoshi
  5. Progress of Theoretical Physics Supplement No.64 (1978) pp. 164-175 :
    Hydrodynamic Instabilities and the Transition to Turbulence
    Harry L. Swinney

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