Intertwined internal rays in Julia sets of rational maps

Robert L. Devaney. "Intertwined internal rays in Julia sets of rational maps." Fundamenta Mathematicae 206.1 (2009): 139-159. <http://eudml.org/doc/283146>.

@article{RobertL2009,
abstract = {We show how the well-known concept of external rays in polynomial dynamics may be extended throughout the Julia set of certain rational maps. These new types of rays, which we call internal rays, meet the Julia set in a Cantor set of points, and each of these rays crosses infinitely many other internal rays at many points. We then use this construction to show that there are infinitely many disjoint copies of the Mandelbrot set in the parameter planes for these maps.},
author = {Robert L. Devaney},
journal = {Fundamenta Mathematicae},
keywords = {internal ray; Julia set; Mandelbrot set; Sierpiński curve},
language = {eng},
number = {1},
pages = {139-159},
title = {Intertwined internal rays in Julia sets of rational maps},
url = {http://eudml.org/doc/283146},
volume = {206},
year = {2009},
}

TY - JOUR
AU - Robert L. Devaney
TI - Intertwined internal rays in Julia sets of rational maps
JO - Fundamenta Mathematicae
PY - 2009
VL - 206
IS - 1
SP - 139
EP - 159
AB - We show how the well-known concept of external rays in polynomial dynamics may be extended throughout the Julia set of certain rational maps. These new types of rays, which we call internal rays, meet the Julia set in a Cantor set of points, and each of these rays crosses infinitely many other internal rays at many points. We then use this construction to show that there are infinitely many disjoint copies of the Mandelbrot set in the parameter planes for these maps.
LA - eng
KW - internal ray; Julia set; Mandelbrot set; Sierpiński curve
UR - http://eudml.org/doc/283146
ER -