Existence of quadratic Hubbard trees

Henk Bruin, Alexandra Kaffl, and Dierk Schleicher. "Existence of quadratic Hubbard trees." Fundamenta Mathematicae 202.3 (2009): 251-279. <http://eudml.org/doc/283172>.

@article{HenkBruin2009,
abstract = {A (quadratic) Hubbard tree is an invariant tree connecting the critical orbit within the Julia set of a postcritically finite (quadratic) polynomial. It is easy to read off the kneading sequences from a quadratic Hubbard tree; the result in this paper handles the converse direction. Not every sequence on two symbols is realized as the kneading sequence of a real or complex quadratic polynomial. Milnor and Thurston classified all real-admissible sequences, and we give a classification of all complex-admissible sequences in [BS]. In order to do this, we show here that every periodic or preperiodic sequence is realized by a unique abstract Hubbard tree. Real or complex admissibility of the sequence depends on whether this abstract tree can be embedded into the real line or complex plane so that the dynamics preserves the embedded, and this can be studied in terms of branch points of the abstract Hubbard tree.},
author = {Henk Bruin, Alexandra Kaffl, Dierk Schleicher},
journal = {Fundamenta Mathematicae},
keywords = {Hubbard tree; kneading theory; kneading sequence; complex dynamics; Julia set; symbolic dynamics},
language = {eng},
number = {3},
pages = {251-279},
title = {Existence of quadratic Hubbard trees},
url = {http://eudml.org/doc/283172},
volume = {202},
year = {2009},
}

TY - JOUR
AU - Henk Bruin
AU - Alexandra Kaffl
AU - Dierk Schleicher
TI - Existence of quadratic Hubbard trees
JO - Fundamenta Mathematicae
PY - 2009
VL - 202
IS - 3
SP - 251
EP - 279
AB - A (quadratic) Hubbard tree is an invariant tree connecting the critical orbit within the Julia set of a postcritically finite (quadratic) polynomial. It is easy to read off the kneading sequences from a quadratic Hubbard tree; the result in this paper handles the converse direction. Not every sequence on two symbols is realized as the kneading sequence of a real or complex quadratic polynomial. Milnor and Thurston classified all real-admissible sequences, and we give a classification of all complex-admissible sequences in [BS]. In order to do this, we show here that every periodic or preperiodic sequence is realized by a unique abstract Hubbard tree. Real or complex admissibility of the sequence depends on whether this abstract tree can be embedded into the real line or complex plane so that the dynamics preserves the embedded, and this can be studied in terms of branch points of the abstract Hubbard tree.
LA - eng
KW - Hubbard tree; kneading theory; kneading sequence; complex dynamics; Julia set; symbolic dynamics
UR - http://eudml.org/doc/283172
ER -