2018-01-21T01:43:33Z
https://digital.csic.es/dspace-oai/request
oai:digital.csic.es:10261/8869
2012-10-10T22:00:00Z
com_10261_113
com_10261_4
col_10261_366
Algorithm for external argument calculation of the nodes of a shrub in the Mandelbrot set
Pastor, Gerardo
Romera, Miguel
Álvarez Marañón, Gonzalo
Arroyo Guardeño, David
Orúe, Amalia B.
Fernández Mármol, Verónica
Montoya Vitini, Fausto
External arguments
Binary expansions
Nodes
Mandelbrot set
Shrub
Misiurewicz points
Nonlinear science
10 pages, 4 figures.
Misiurewicz points are essential points of the Mandelbrot set. External arguments are the most useful tool in order to analyze these points; therefore, it is important to go deeper in the study of the external arguments' calculation of these points. In this paper we introduce an algorithm to calculate the external arguments of the branch points, or nodes, of a shrub, since such nodes are the most outstanding Misiurewicz points of the chaotic region of the Mandelbrot set. Devaney and Moreno-Rocha had already presented a paper where they calculated the external arguments of one of these Misiurewicz points, the main node of a shrub. Our algorithm widens the study of Devaney and Moreno-Rocha because it allows one to calculate the external arguments of any node of the shrub.
This work was partially supported by: (a) MEC of Spain, research grant TSI 2007-62657; (b) CDTI, MITYC of Spain, SAC, Project Hesperia; (c) CDTI, MITYC of Spain, Telefonica I+D Project Segur@.
Peer reviewed
2008-11-27T16:28:03Z
2008-11-27T16:28:03Z
2008-06
Artículo
Fractals 16(2): 159-168 (2008)
0218-348X
http://hdl.handle.net/10261/8869
10.1142/S0218348X08003855
eng
http://dx.doi.org/10.1142/S0218348X08003855
closedAccess
191554 bytes
application/pdf
World Scientific Publishing