We prove that for some families of entire functions whose Julia set is the complement of the basin of attraction every branch of a tree of preimages starting from this basin is convergent.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm180-1-5, author = {Bogus\l awa Karpi\'nska}, title = {On the accessible points in the Julia sets of some entire functions}, journal = {Fundamenta Mathematicae}, volume = {177}, year = {2003}, pages = {89-98}, zbl = {1047.37029}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm180-1-5} }
Bogusława Karpińska. On the accessible points in the Julia sets of some entire functions. Fundamenta Mathematicae, Tome 177 (2003) pp. 89-98. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm180-1-5/