A note on the structure of quadratic Julia sets

Karsten Keller

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 2, page 395-406
  • ISSN: 0010-2628

Abstract

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In a series of papers, Bandt and the author have given a symbolic and topological description of locally connected quadratic Julia sets by use of special closed equivalence relations on the circle called Julia equivalences. These equivalence relations reflect the landing behaviour of external rays in the case of local connectivity, and do not apply completely if a Julia set is connected but fails to be locally connected. However, rational external rays land also in the general case. The present note shows that for a quadratic map which does not possess an irrational indifferent periodic orbit and has a connected Julia set the following holds: The equivalence relation induced by the landing behaviour of rational external rays forms the rational part of a Julia equivalence.

How to cite

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Keller, Karsten. "A note on the structure of quadratic Julia sets." Commentationes Mathematicae Universitatis Carolinae 38.2 (1997): 395-406. <http://eudml.org/doc/248098>.

@article{Keller1997,
abstract = {In a series of papers, Bandt and the author have given a symbolic and topological description of locally connected quadratic Julia sets by use of special closed equivalence relations on the circle called Julia equivalences. These equivalence relations reflect the landing behaviour of external rays in the case of local connectivity, and do not apply completely if a Julia set is connected but fails to be locally connected. However, rational external rays land also in the general case. The present note shows that for a quadratic map which does not possess an irrational indifferent periodic orbit and has a connected Julia set the following holds: The equivalence relation induced by the landing behaviour of rational external rays forms the rational part of a Julia equivalence.},
author = {Keller, Karsten},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {quadratic Julia set; Julia equivalence; external ray; quadratic Julia set; Julia equivalence; external ray},
language = {eng},
number = {2},
pages = {395-406},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A note on the structure of quadratic Julia sets},
url = {http://eudml.org/doc/248098},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Keller, Karsten
TI - A note on the structure of quadratic Julia sets
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 2
SP - 395
EP - 406
AB - In a series of papers, Bandt and the author have given a symbolic and topological description of locally connected quadratic Julia sets by use of special closed equivalence relations on the circle called Julia equivalences. These equivalence relations reflect the landing behaviour of external rays in the case of local connectivity, and do not apply completely if a Julia set is connected but fails to be locally connected. However, rational external rays land also in the general case. The present note shows that for a quadratic map which does not possess an irrational indifferent periodic orbit and has a connected Julia set the following holds: The equivalence relation induced by the landing behaviour of rational external rays forms the rational part of a Julia equivalence.
LA - eng
KW - quadratic Julia set; Julia equivalence; external ray; quadratic Julia set; Julia equivalence; external ray
UR - http://eudml.org/doc/248098
ER -

References

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