Chaotic behavior and fluid dynamics

  • J. A. Yorke
  • E. D. Yorke
Part of the Topics in Applied Physics book series (TAP, volume 45)


Initial Data Steady Flow Chaotic Behavior Couette Flow Strange Attractor 
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  1. 4.1
    D. Ruelle: “Dynamical Systems with Turbulent Behavior”, in Mathematical Problems in Theoretical Physics, Lecture Notes in Physics, Vol. 80 (Springer, Berlin, Heidelberg, New York 1978) p. 341Google Scholar
  2. 4.2
    D. Ruelle: Sensitive dependence on initial condition and turbulent behavior of dynamical systems. Ann. N.Y. Acad. Sci. 316, 408 (1979)Google Scholar
  3. 4.3.
    E. N. Lorenz: Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130 (1963)Google Scholar
  4. 4.4
    B. Saltzman: Finite amplitude free convection as an initial value problem, I. J. Atmos. Sci. 19, 329 (1962)Google Scholar
  5. 4.5
    J. L. Kaplan, J. A. Yorke: Preturbulence: a regime observed in a fluid flow model of Lorenz. Commun. Math. Phys. 67, 93–108 (1979)Google Scholar
  6. 4.6
    J. A. Yorke, E. D. Yorke: Metastable chaos: the transition to sustained chaotic behavior in the Lorenz model. J. Statist. Phys. 21, 263–277 (1979)Google Scholar
  7. 4.7
    J. B. Mc Laughlin, P. C. Martin: Transition to turbulence in a statically stressed fluid system. Phys. Rev. A 12, 186 (1975)Google Scholar
  8. 4.8
    J. H. Curry: Ph.D. Dissertation, University of California, Berkeley (1976)Google Scholar
  9. 4.9
    W. V. R. Malkus: Mém. Soc. Royale de Sci. de Liège, 6th Ser. 4, 125 (1972)Google Scholar
  10. 4.10
    L. A. Rubenfeld, W. L. Siegman: Nonlinear dynamic theory for a double-diffusive convection model. SIAM J. Appl. Math. 32, 871 (1977)Google Scholar
  11. 4.11
    P. Welander: On the oscillatory instability of a differentially heated fluid loop. J. Fluid Mech. 29, 17 (1967)Google Scholar
  12. 4.12
    H. F. Creveling, J. F. dePaz, J. Y. Baladi, R. J. Schoenhals: Stability characteristics of a singlephase free convection loop. J. Fluid Mech. 67, 65 (1975)Google Scholar
  13. 4.13
    D. Ruelle, F. Takens: On the nature of turbulence. Commun. Math. Phys. 20,167 (1971); 23, 343 (1971)Google Scholar
  14. 4.14
    J. K. Moser: On a theorem of Anasov. J. Differ. Equat. 5, 411 (1969)Google Scholar
  15. 4.15
    J. L. Kaplan, J. A. Yorke: “Chaotic behavior of multidimensional difference equations”, in Functional Differential Equations and Approximations of Fixed Points, Lecture Notes in Mathematics, Vol. 730, ed. by H. O. Peitgen, H. O. Walther (Springer, Berlin, Heidelberg, New York 1979) pp. 228–237Google Scholar
  16. 4.16
    J. Curry, J. A. Yorke: “A Transition from Hopf Bifurcation to Chaos: Computer Experiments with Maps in ℝ2”, in The Structure of Attractors in Dynamical Systems, Springer Notes in Mathematics, Vol. 668 (Springer, Berlin, Heidelberg, New York 1977) p. 48Google Scholar
  17. 4.17
    J. Guckenheimer: “Structural stability of the Lorenz attractor”, Institut des Hautes Études Scientifiques, Publications Mathématiques No. 50 (1980)Google Scholar
  18. 4.18
    J. Guckenheimer, R. F. Williams: The structure of Lorenz attractors. Appl. Math. Sci. 19, 368–381 (1976)Google Scholar
  19. 4.19
    L. Landau, L. Lifschitz: Fluid Mechanics (Pergamon, Oxford 1959)Google Scholar
  20. 4.20
    J. L. Kaplan, J. A. Yorke: The onset of turbulence in a fluid flow model of Lorenz. Ann. N. Y. Acad. Sci. 316, 400 (1979)Google Scholar
  21. 4.21
    T. Y. Li, J. A. Yorke: Period three implies chaos. Amer. Math. Mon. 82, 985 (1975)Google Scholar
  22. 4.22
    R. M. May: Simple mathematical models with very complicated dynamics. Nature 261, 459 (1976). See also R.M. May: Bifurcations and dynamic complexity in ecological systems. Ann. N.Y. Acad. Sci. 316, 517 (1979)Google Scholar
  23. 4.23
    O. Rössler: Continuous chaos–four prototype equations. Ann. N.Y. Acad. Sci. 316, 376 (1979)Google Scholar
  24. 4.24.
    J.-M. Wersinger, J. M. Finn, E. Ott: Bifurcation and “Strange” Behavior in Instability Saturation by Nonlinear Three Wave Mode Coupling. Phys. Fluids 23, 1142 (1980)Google Scholar
  25. 4.25
    A. N. Sharkovskii: Coexistence of the cycles of a continuous mapping of the line into itself (Russian). Ukr. Math. J. 16, No. 1, 61 (1964)Google Scholar
  26. 4.26
    R. Bowen: “A Model for Couette Flow Data”, in Berkeley Turbulence Seminar, Lecture Notes in Mathematics, Vol. 615 (Springer, Berlin, Heidelberg, New York 1977 p. 117Google Scholar
  27. 4.27
    M. Lucke: Statistical dynamics of the Lorenz model. J. Stat. Phys. 15, 455 (1976)Google Scholar
  28. 4.28
    T. Y. Li, J. A. Yorke: Ergodic transformations from an interval into itself. Trans. Am. Math. Soc. 235, 183 (1978)Google Scholar
  29. 4.29
    A A. Kosygin, E. A. Sandier: Izv. Vyss. Ucebn. Zaved. Mat. 118, 32 (1972)Google Scholar
  30. 4.30
    G. Pianigiani: Existence of Invariant Measures for Piecewise Continuous Transformations. Ann. Polon. Math. (to appear)Google Scholar
  31. 4.31
    S. Wong: Some Metric Properties of Piecewise Monotonic Mappings of the Unit Interval. Trans. Math. Soc. 252, 351 (1979)Google Scholar
  32. 4.32
    R. Bowen, D. Ruelle: The ergodic theory of axiom A attractors. Invent. Math. 29, 181 (1975)Google Scholar
  33. 4.33
    A.Lasota, J.A.Yorke: The Law of Exponential Decay for Expanding Maps. Rendiconti Padova (in press)Google Scholar

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© Springer-Verlag 1981

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  • J. A. Yorke
  • E. D. Yorke

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