We prove that if A is a basin of immediate attraction to a periodic attracting or parabolic point for a rational map f on the Riemann sphere, then the periodic points in the boundary of A are dense in this boundary. To prove this in the non-simply connected or parabolic situations we prove a more abstract, geometric coding trees version.
@article{bwmeta1.element.bwnjournal-article-fmv145i1p65bwm,
author = {Feliks Przytycki and Anna Zdunik},
title = {Density of periodic sources in the boundary of a basin of attraction for iteration of holomorphic maps: geometric coding trees technique},
journal = {Fundamenta Mathematicae},
volume = {144},
year = {1994},
pages = {65-77},
zbl = {0817.58033},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv145i1p65bwm}
}
Przytycki, Feliks; Zdunik, Anna. Density of periodic sources in the boundary of a basin of attraction for iteration of holomorphic maps: geometric coding trees technique. Fundamenta Mathematicae, Tome 144 (1994) pp. 65-77. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv145i1p65bwm/
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