A combinatorial invariant for escape time Sierpiński rational maps

Mónica Moreno Rocha

Fundamenta Mathematicae (2013)

  • Volume: 222, Issue: 2, page 99-130
  • ISSN: 0016-2736

Abstract

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An escape time Sierpiński map is a rational map drawn from the McMullen family z ↦ zⁿ + λ/zⁿ with escaping critical orbits and Julia set homeomorphic to the Sierpiński curve continuum. We address the problem of characterizing postcritically finite escape time Sierpiński maps in a combinatorial way. To accomplish this, we define a combinatorial model given by a planar tree whose vertices come with a pair of combinatorial data that encodes the dynamics of critical orbits. We show that each escape time Sierpiński map realizes a subgraph of the combinatorial tree and the combinatorial information is a complete conjugacy invariant.

How to cite

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Mónica Moreno Rocha. "A combinatorial invariant for escape time Sierpiński rational maps." Fundamenta Mathematicae 222.2 (2013): 99-130. <http://eudml.org/doc/282700>.

@article{MónicaMorenoRocha2013,
abstract = { An escape time Sierpiński map is a rational map drawn from the McMullen family z ↦ zⁿ + λ/zⁿ with escaping critical orbits and Julia set homeomorphic to the Sierpiński curve continuum. We address the problem of characterizing postcritically finite escape time Sierpiński maps in a combinatorial way. To accomplish this, we define a combinatorial model given by a planar tree whose vertices come with a pair of combinatorial data that encodes the dynamics of critical orbits. We show that each escape time Sierpiński map realizes a subgraph of the combinatorial tree and the combinatorial information is a complete conjugacy invariant. },
author = {Mónica Moreno Rocha},
journal = {Fundamenta Mathematicae},
keywords = {rational maps; Julia sets; combinatorial invariants},
language = {eng},
number = {2},
pages = {99-130},
title = {A combinatorial invariant for escape time Sierpiński rational maps},
url = {http://eudml.org/doc/282700},
volume = {222},
year = {2013},
}

TY - JOUR
AU - Mónica Moreno Rocha
TI - A combinatorial invariant for escape time Sierpiński rational maps
JO - Fundamenta Mathematicae
PY - 2013
VL - 222
IS - 2
SP - 99
EP - 130
AB - An escape time Sierpiński map is a rational map drawn from the McMullen family z ↦ zⁿ + λ/zⁿ with escaping critical orbits and Julia set homeomorphic to the Sierpiński curve continuum. We address the problem of characterizing postcritically finite escape time Sierpiński maps in a combinatorial way. To accomplish this, we define a combinatorial model given by a planar tree whose vertices come with a pair of combinatorial data that encodes the dynamics of critical orbits. We show that each escape time Sierpiński map realizes a subgraph of the combinatorial tree and the combinatorial information is a complete conjugacy invariant.
LA - eng
KW - rational maps; Julia sets; combinatorial invariants
UR - http://eudml.org/doc/282700
ER -

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