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An Introduction to Dynamical Systems and Chaos pp 575–618Cite as

Fractals

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Abstract

With the advent of civilization human mind always tend to unravel the wealth of knowledge in nature, whether it is his curiosity to know the universe or to measure the length of the coastlines of the earth. However, despite discovering modern technological tools, most of the knowledge remains unknown.

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References

  1. Cantor, G.: Über unendliche, lineare Punktmannigfaltigkeiten V. Math. Ann. 21, 545–591 (1883)

    Article  MathSciNet  MATH  Google Scholar 

  2. von Koch, H.: Sur une courbe continue sans tangente, obtenue par une construction géometrique élémentaire. Arkiv för Matematik 1, 681–704 (1904)

    MATH  Google Scholar 

  3. von Koch, H.: Une méthode géométrique élémentaire pour l’étude de certaines questions de la théorie des courbes planes. Acta Mathematica 30, 145–174 (1906)

    Article  MathSciNet  MATH  Google Scholar 

  4. Sierpinski, W.: Sur une courbe cantorienne dont tout point est un point de ramification. C. R. Acad. Paris 160, 302 (1915)

    MATH  Google Scholar 

  5. Sierpinski, W.: Sur une courbe cantorienne qui contient une image biunivoquet et continue detoute courbe donnée. C. R. Acad. Paris 162, 629–632 (1916)

    MATH  Google Scholar 

  6. Julia, G.: Mémoire sur l’iteration des fonctions rationnelles. J. de Math. Pure et Appl. 8, 47–245 (1918)

    MATH  Google Scholar 

  7. Benoit, B.: Mandelbrot: Fractal aspects of the iteration z ⟼λ z(1 – z) of for complex λ and z and Annals NY Acad. Sciences 357, 249–259 (1980)

    Google Scholar 

  8. Grassberger, P., Procaccia, I.: Characterization of strange attractors. Phys. Rev. Lett. 50, 346 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  9. Ruelle, D., Takens, F.: On the nature of turbulence. Commun. Math. Phys. 20, 167–192; 23, 343–344 (1971)

    Google Scholar 

  10. Arnold, V.I., Avez, A.: Ergodic problems in classical mechanics. Benjamin, New York (1968)

    MATH  Google Scholar 

  11. Ya, G.: Sinai: Self-similar probability distributions. Theor. Probab. Appl. 21, 64–80 (1976)

    Article  Google Scholar 

  12. Hénon, M.: A Two-dimensional Mapping with a Strange Attractor. Commun. Math. Phys. 50, 69–77 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  13. Alligood, K.T., Sauer, T.D, Yorke, J.A.: Chaos: An Introduction to Dynamical Systems. Springer (1997)

    Google Scholar 

  14. Otto, E.: Rössler: An equation for continuous chaos. Phys. Lett. 57A, 5 (1976)

    Google Scholar 

  15. Benoit, B.: Mandelbrot: The fractal geometry of nature. W. H. Freeman and Company, New York (1977)

    Google Scholar 

  16. Peitgen, Heinz-Otto: Hartmut Jürgens, Dietmar Saupe: Chaos and fractals. Springer-Verlag, New York (2004)

    Google Scholar 

  17. Falconer, K.: Fractal geometry, Mathematical foundations and applications. Wiley, New York (1990)

    MATH  Google Scholar 

  18. Lorenz, E.N.: Deterministic non-periodic flow. J. Atmos. Sci. 20, 130–141 (1963)

    Article  Google Scholar 

  19. Strogatz, S.H.: Nonlinear Dynamics and Chaos with application to physics, biology, chemistry and engineering. Perseus books, L.L.C, Massachusetts (1994)

    Google Scholar 

  20. Benoit, B.: Mandelbrot: How long is the coast of Britain? Science 156, 636–638 (1967)

    Article  Google Scholar 

  21. Oberlack, M.: A unified approach for symmetries in plane parallel turbulent shear flows. J. Fluid Mech. 427, 299–328 (2001)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, The University of Burdwan, Burdwan, West Bengal, India

    G. c. Layek

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  1. G. c. Layek
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Correspondence to G. c. Layek .

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Layek, G.c. (2015). Fractals. In: An Introduction to Dynamical Systems and Chaos. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2556-0_13

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