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Discrete Dynamics in Nature and Society
Volume 2007 (2007), Article ID 45920, 17 pages
http://dx.doi.org/10.1155/2007/45920
Research Article

Operating with External Arguments of Douady and Hubbard

Instituto de Física Aplicada, Consejo Superior de Investigaciones Científicas, Serrano 144, Madrid 28006, Spain

Received 22 May 2007; Accepted 22 September 2007

Copyright © 2007 G. Pastor et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. B. Branner, “The Mandelbrot set,” in Chaos and Fractals, vol. 39 of Proceedings Symposium Applied Mathematics, pp. 75–105, American Mathematical Society, Providence, RI, USA, 1989. View at Google Scholar · View at MathSciNet
  2. M. Misiurewicz and Z. Nitecki, “Combinatorial patterns for maps of the interval,” Memoirs of the American Mathematical Society, vol. 94, no. 456, p. 112, 1991. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. G. Pastor, M. Romera, and F. Montoya, “On the calculation of Misiurewicz patterns in one-dimensional quadratic maps,” Physica A, vol. 232, no. 1-2, pp. 536–553, 1996. View at Publisher · View at Google Scholar
  4. M. Romera, G. Pastor, and F. Montoya, “Misiurewicz points in one-dimensional quadratic maps,” Physica A, vol. 232, no. 1-2, pp. 517–535, 1996. View at Publisher · View at Google Scholar
  5. G. Pastor, M. Romera, G. Alvarez, and F. Montoya, “Operating with external arguments in the Mandelbrot set antenna,” Physica D, vol. 171, no. 1-2, pp. 52–71, 2002. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. G. Pastor, M. Romera, G. Alvarez, and F. Montoya, “External arguments for the chaotic bands calculation in the Mandelbrot set,” Physica A, vol. 353, pp. 145–158, 2005. View at Publisher · View at Google Scholar
  7. A. Douady and J. H. Hubbard, “Itération des polynômes quadratiques complexes,” Comptes Rendus des Séances de l'Académie des Sciences, vol. 294, no. 3, pp. 123–126, 1982. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. G. Pastor, M. Romera, and F. Montoya, “Harmonic structure of one-dimensional quadratic maps,” Physical Review E, vol. 56, no. 2, pp. 1476–1483, 1997. View at Publisher · View at Google Scholar
  9. W. Jung, Programs for dynamical systems, http://www.iram.rwth-aachen.de/~jung/indexp.html.
  10. R. L. Devaney, “The complex dynamics of quadratic polynomials,” in Complex Dynamical Systems, R. L. Devaney, Ed., vol. 49 of Proceedings Symposium Applied Mathematics, pp. 1–29, American Mathematical Society, Cincinnati, Ohio, USA, 1994. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. A. Douady, “Algorithms for computing angles in the Mandelbrot set,” in Chaotic Dynamics and Fractals, M. Barnsley and S. G. Demko, Eds., vol. 2 of Notes and Reports in Mathematics in Science and Engineering, pp. 155–168, Academic Press, Atlanta, Ga, USA, 1986. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. M. Romera, G. Pastor, G. Alvarez, and F. Montoya, “Shrubs in the Mandelbrot set ordering,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 13, no. 8, pp. 2279–2300, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. G. Pastor, M. Romera, G. Alvarez, D. Arroyo, and F. Montoya, “Equivalence between subshrubs and chaotic bands in the Mandelbrot set,” Discrete Dynamics in Nature and Society, vol. 2006, Article ID 70471, 25 pages, 2006. View at Google Scholar · View at MathSciNet
  14. E. Lau and D. Schleicher, “Internal addresses in the Mandelbrot set and irreducibility of polynomials,” http://www.math.sunysb.edu/cgi-bin/preprint.pl?ims94-19.