• G. c. LayekEmail author


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.


Periodic Point Euclidean Geometry Strange Attractor Fractal Object Lorenz Attractor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Cantor, G.: Über unendliche, lineare Punktmannigfaltigkeiten V. Math. Ann. 21, 545–591 (1883)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    von Koch, H.: Sur une courbe continue sans tangente, obtenue par une construction géometrique élémentaire. Arkiv för Matematik 1, 681–704 (1904)zbMATHGoogle Scholar
  3. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Sierpinski, W.: Sur une courbe cantorienne dont tout point est un point de ramification. C. R. Acad. Paris 160, 302 (1915)zbMATHGoogle Scholar
  5. 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)zbMATHGoogle Scholar
  6. 6.
    Julia, G.: Mémoire sur l’iteration des fonctions rationnelles. J. de Math. Pure et Appl. 8, 47–245 (1918)zbMATHGoogle Scholar
  7. 7.
    Benoit, B.: Mandelbrot: Fractal aspects of the iteration zλ z(1 – z) of for complex λ and z and Annals NY Acad. Sciences 357, 249–259 (1980)Google Scholar
  8. 8.
    Grassberger, P., Procaccia, I.: Characterization of strange attractors. Phys. Rev. Lett. 50, 346 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Ruelle, D., Takens, F.: On the nature of turbulence. Commun. Math. Phys. 20, 167–192; 23, 343–344 (1971)Google Scholar
  10. 10.
    Arnold, V.I., Avez, A.: Ergodic problems in classical mechanics. Benjamin, New York (1968)zbMATHGoogle Scholar
  11. 11.
    Ya, G.: Sinai: Self-similar probability distributions. Theor. Probab. Appl. 21, 64–80 (1976)CrossRefGoogle Scholar
  12. 12.
    Hénon, M.: A Two-dimensional Mapping with a Strange Attractor. Commun. Math. Phys. 50, 69–77 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Alligood, K.T., Sauer, T.D, Yorke, J.A.: Chaos: An Introduction to Dynamical Systems. Springer (1997)Google Scholar
  14. 14.
    Otto, E.: Rössler: An equation for continuous chaos. Phys. Lett. 57A, 5 (1976)Google Scholar
  15. 15.
    Benoit, B.: Mandelbrot: The fractal geometry of nature. W. H. Freeman and Company, New York (1977)Google Scholar
  16. 16.
    Peitgen, Heinz-Otto: Hartmut Jürgens, Dietmar Saupe: Chaos and fractals. Springer-Verlag, New York (2004)Google Scholar
  17. 17.
    Falconer, K.: Fractal geometry, Mathematical foundations and applications. Wiley, New York (1990)zbMATHGoogle Scholar
  18. 18.
    Lorenz, E.N.: Deterministic non-periodic flow. J. Atmos. Sci. 20, 130–141 (1963)CrossRefGoogle Scholar
  19. 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. 20.
    Benoit, B.: Mandelbrot: How long is the coast of Britain? Science 156, 636–638 (1967)CrossRefGoogle Scholar
  21. 21.
    Oberlack, M.: A unified approach for symmetries in plane parallel turbulent shear flows. J. Fluid Mech. 427, 299–328 (2001)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer India 2015

Authors and Affiliations

  1. 1.Department of MathematicsThe University of BurdwanBurdwanIndia

Personalised recommendations