calculation of the structure of a shrub in the mandelbrot set

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ID: 183897
2011
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Abstract
We calculate the external arguments of the structure of any shrub in the Mandelbrot set. Before calculating, we revise, expand, and clarify some tools useful for this paper: harmonics, pseudoharmonics, the concept of structure, the structure of a shrub, and the ancestral route. Finally we present the main contribution of this paper, a three-step algorithm which allows us to calculate the structure of the shrub. In the first step, we use pseudoharmonics that were previously introduced by us, in order to calculate the first and last external arguments of a structural node. In the second step, starting from two general properties of the Misiurewicz points external arguments introduced here by us, we present a new method to calculate the intermediate external arguments. In the last step we introduce a third property that allows us to calculate the external arguments of the representatives of the branches emerging from the structural nodes.
Reference Key
pastor2011discretecalculation Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;G. Pastor;M. Romera;A. B. Orue;A. Martín;M-F. Danca;F. Montoya
Journal Journal of the American Heart Association
Year 2011
DOI
10.1155/2011/837262
URL
http://dx.doi.org/10.1155/2011/837262
Keywords
mathematics

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