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Lecture V Fractals and turbulence: Attractors and dispersion

Part of the Lecture Notes in Mathematics book series (LNM,volume 615)

Keywords

  • Fractal Dimension
  • Topological Dimension
  • Construction Stage
  • Fractal Curve
  • Homogeneous Turbulence

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References

  • Adler, R.J. 1977. Hausdorff dimension and Gaussian fields. The Annals of Probability, Vol. 5, 145–151.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Berger, J.M. & Mandelbrot, B.B. 1963. A new model for the clustering of errors on telephone circuits. IBM Journal of Research and Development, Vol. 7, 224–236.

    CrossRef  Google Scholar 

  • Billingsley, P. 1967. Ergodic Theory and Information. New York: Wiley.

    MATH  Google Scholar 

  • Hurewicz, W. & Wallman, H. 1941. Dimension Theory. Princeton University Press.

    Google Scholar 

  • Kolmogorov, A.N. 1962. A refinement of previous hypotheses concerning the local structures of turbulence in a viscous incompressible fluid at high Reynolds number. Journal of Fluid Mechanics, Vol. 13, 82–85.

    CrossRef  MathSciNet  MATH  Google Scholar 

  • Lorenz, E.N. 1963. Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, Vol. 20, 130–141.

    CrossRef  Google Scholar 

  • Mandelbrot, B.B. 1975. Les objets fractals: forme, hasard et dimension. Paris and Montreal: Flammarion.

    Google Scholar 

  • Mandelbrot, B.B. 1976. Intermittent turbulence and fractal dimension: kurtosis and the spectral exponent 5/3+B. In Turbulence and Navier Stokes Equations, 121–145. Ed. R. Teman. Lecture Notes in Mathematics 565. New York: Springer.

    CrossRef  Google Scholar 

  • Mandelbrot, B.B. 1977. Fractals: form, chance, and dimension. San Francisco: W.H. Freeman and Company.

    MATH  Google Scholar 

  • Novikov, E.A. & Stewart, R.W. 1964. Intermittency of turbulence and the spectrum of fluctuations of energy dissipation. (in Russian) Isvestia Akademii Nauk SSR; Seria Geofizicheskaia, Vol. 3, 408–413.

    Google Scholar 

  • Ruelle, D. & Takens, F. 1971. On the nature of turbulence. Communications on Mathematical Physics, Vol. 20, 167–192 & Vol. 23, 343–344.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1977 Springer-Verlag

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Mandelbrot, B.B. (1977). Lecture V Fractals and turbulence: Attractors and dispersion. In: Bernard, P., Ratiu, T. (eds) Turbulence Seminar. Lecture Notes in Mathematics, vol 615. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068362

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  • DOI: https://doi.org/10.1007/BFb0068362

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08445-7

  • Online ISBN: 978-3-540-37074-1

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