On biaccessible points in Julia sets of polynomials

Anna Zdunik

Fundamenta Mathematicae (2000)

  • Volume: 163, Issue: 3, page 277-286
  • ISSN: 0016-2736

Abstract

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Let f be a polynomial of one complex variable so that its Julia set is connected. We show that the harmonic (Brolin) measure of the set of biaccessible points in J is zero except for the case when J is an interval.

How to cite

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Zdunik, Anna. "On biaccessible points in Julia sets of polynomials." Fundamenta Mathematicae 163.3 (2000): 277-286. <http://eudml.org/doc/212444>.

@article{Zdunik2000,
abstract = {Let f be a polynomial of one complex variable so that its Julia set is connected. We show that the harmonic (Brolin) measure of the set of biaccessible points in J is zero except for the case when J is an interval.},
author = {Zdunik, Anna},
journal = {Fundamenta Mathematicae},
keywords = {harmonic Brolin measure; Julia sets},
language = {eng},
number = {3},
pages = {277-286},
title = {On biaccessible points in Julia sets of polynomials},
url = {http://eudml.org/doc/212444},
volume = {163},
year = {2000},
}

TY - JOUR
AU - Zdunik, Anna
TI - On biaccessible points in Julia sets of polynomials
JO - Fundamenta Mathematicae
PY - 2000
VL - 163
IS - 3
SP - 277
EP - 286
AB - Let f be a polynomial of one complex variable so that its Julia set is connected. We show that the harmonic (Brolin) measure of the set of biaccessible points in J is zero except for the case when J is an interval.
LA - eng
KW - harmonic Brolin measure; Julia sets
UR - http://eudml.org/doc/212444
ER -

References

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  8. [Po] C. Pommerenke, Boundary Behaviour of Conformal Maps, Springer, Berlin, 1992. Zbl0762.30001
  9. [P] F. Przytycki, Remarks on simple connectedness of basins of sinks for iterations of rational maps, in: Banach Center Publ. 23, PWN, 1989, 229-235. Zbl0703.58033
  10. [PUbook] F. Przytycki and M. Urbański, Fractals in the Plane-Ergodic Theory Methods, to appear; preliminary version at www.math.unt.edu/urbanski. 
  11. [Th] W. Thurston, On the dynamics of iterated rational maps, preprint. 
  12. [Za] S. Zakeri, Biaccessibility in quadratic Julia sets, I: the locally connected case, preprint SUNY, Stony Brook, 1998. 
  13. [Z] A. Zdunik, Parabolic orbifolds and the dimension of the maximal measure for rational maps, Invent. Math. 99 (1990), 627-649. Zbl0820.58038

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