Equivalence between subshrubs and chaotic bands in the Mandelbrot set
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, w...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2006-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/DDNS/2006/70471 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 1026-0226 1607-887X |