Dynamics on Hubbard trees

Lluís Alsedà; Núria Fagella

Fundamenta Mathematicae (2000)

  • Volume: 164, Issue: 2, page 115-141
  • ISSN: 0016-2736

Abstract

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It is well known that the Hubbard tree of a postcritically finite complex polynomial contains all the combinatorial information on the polynomial. In fact, an abstract Hubbard tree as defined in [23] uniquely determines the polynomial up to affine conjugation. In this paper we give necessary and sufficient conditions enabling one to deduce directly from the restriction of a quadratic Misiurewicz polynomial to its Hubbard tree whether the polynomial is renormalizable, and in this case, of which type. Moreover, we study dynamical features such as entropy, transitivity or periodic structure of the polynomial restricted to the Hubbard tree, and compare them with the properties of the polynomial on its Julia set. In other words, we want to study how much of the "dynamical information" about the polynomial is captured by the Hubbard tree.

How to cite

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Alsedà, Lluís, and Fagella, Núria. "Dynamics on Hubbard trees." Fundamenta Mathematicae 164.2 (2000): 115-141. <http://eudml.org/doc/212450>.

@article{Alsedà2000,
abstract = {It is well known that the Hubbard tree of a postcritically finite complex polynomial contains all the combinatorial information on the polynomial. In fact, an abstract Hubbard tree as defined in [23] uniquely determines the polynomial up to affine conjugation. In this paper we give necessary and sufficient conditions enabling one to deduce directly from the restriction of a quadratic Misiurewicz polynomial to its Hubbard tree whether the polynomial is renormalizable, and in this case, of which type. Moreover, we study dynamical features such as entropy, transitivity or periodic structure of the polynomial restricted to the Hubbard tree, and compare them with the properties of the polynomial on its Julia set. In other words, we want to study how much of the "dynamical information" about the polynomial is captured by the Hubbard tree.},
author = {Alsedà, Lluís, Fagella, Núria},
journal = {Fundamenta Mathematicae},
keywords = {Hubbard trees; renormalization; Misiurewicz polynomials; transitivity; topological entropy},
language = {eng},
number = {2},
pages = {115-141},
title = {Dynamics on Hubbard trees},
url = {http://eudml.org/doc/212450},
volume = {164},
year = {2000},
}

TY - JOUR
AU - Alsedà, Lluís
AU - Fagella, Núria
TI - Dynamics on Hubbard trees
JO - Fundamenta Mathematicae
PY - 2000
VL - 164
IS - 2
SP - 115
EP - 141
AB - It is well known that the Hubbard tree of a postcritically finite complex polynomial contains all the combinatorial information on the polynomial. In fact, an abstract Hubbard tree as defined in [23] uniquely determines the polynomial up to affine conjugation. In this paper we give necessary and sufficient conditions enabling one to deduce directly from the restriction of a quadratic Misiurewicz polynomial to its Hubbard tree whether the polynomial is renormalizable, and in this case, of which type. Moreover, we study dynamical features such as entropy, transitivity or periodic structure of the polynomial restricted to the Hubbard tree, and compare them with the properties of the polynomial on its Julia set. In other words, we want to study how much of the "dynamical information" about the polynomial is captured by the Hubbard tree.
LA - eng
KW - Hubbard trees; renormalization; Misiurewicz polynomials; transitivity; topological entropy
UR - http://eudml.org/doc/212450
ER -

References

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