Dynamics on Hubbard trees
Fundamenta Mathematicae, Tome 164 (2000) no. 2, pp. 115-141
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
Hubbard trees, renormalization, Misiurewicz polynomials, transitivity, topological entropy
Affiliations des auteurs :
Lluís Alsedà 1 ; Núria Fagella 1
@article{10_4064_fm_164_2_115_141,
author = {Llu{\'\i}s Alsed\`a and N\'uria Fagella},
title = {Dynamics on {Hubbard} trees},
journal = {Fundamenta Mathematicae},
pages = {115--141},
year = {2000},
volume = {164},
number = {2},
doi = {10.4064/fm-164-2-115-141},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-164-2-115-141/}
}
Lluís Alsedà; Núria Fagella. Dynamics on Hubbard trees. Fundamenta Mathematicae, Tome 164 (2000) no. 2, pp. 115-141. doi: 10.4064/fm-164-2-115-141
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