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Equivalence between subshrubs and chaotic bands in the Mandelbrot set

Author

Listed:
  • G. Pastor
  • M. Romera
  • G. Alvarez
  • D. Arroyo
  • F. Montoya

Abstract

We study in depth the equivalence between subshrubs and chaotic bands in the Mandelbrot set. In order to do so, we introduce the rules for chaotic bands and the rules for subshrubs, as well as the transformation rules that allow us to interchange them. From all the denominations of a chaotic band, we show the canonical form; that is, the one associated to the hyperbolic component that generates such a chaotic band. Starting from the study of the one-dimensional route, we fulfil an inductive study that gives a generalization of the shrub concept.

Suggested Citation

  • G. Pastor & M. Romera & G. Alvarez & D. Arroyo & F. Montoya, 2006. "Equivalence between subshrubs and chaotic bands in the Mandelbrot set," Discrete Dynamics in Nature and Society, Hindawi, vol. 2006, pages 1-25, August.
    • Handle: RePEc:hin:jnddns:070471
    DOI: 10.1155/DDNS/2006/70471
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