Dimension of the harmonic measure of non-homogeneous Cantor sets

Athanasios Batakis[1]

  • [1] Université d’Orléans Département de Mathématiques MAPMO BP 6759 45067 Orléans cedex 2 (France)

Annales de l’institut Fourier (2006)

  • Volume: 56, Issue: 6, page 1617-1631
  • ISSN: 0373-0956

Abstract

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We prove that the dimension of the harmonic measure of the complementary of a translation-invariant type of Cantor sets is a continuous function of the parameters determining these sets. This results extends a previous one of the author and do not use ergotic theoretic tools, not applicables to our case.

How to cite

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Batakis, Athanasios. "Dimension of the harmonic measure of non-homogeneous Cantor sets." Annales de l’institut Fourier 56.6 (2006): 1617-1631. <http://eudml.org/doc/10186>.

@article{Batakis2006,
abstract = {We prove that the dimension of the harmonic measure of the complementary of a translation-invariant type of Cantor sets is a continuous function of the parameters determining these sets. This results extends a previous one of the author and do not use ergotic theoretic tools, not applicables to our case.},
affiliation = {Université d’Orléans Département de Mathématiques MAPMO BP 6759 45067 Orléans cedex 2 (France)},
author = {Batakis, Athanasios},
journal = {Annales de l’institut Fourier},
keywords = {Harmonic measure; Cantor sets; fractals; Hausdorff dimension; entropy; harmonic measure; Cantor set; exact measure; code space},
language = {eng},
number = {6},
pages = {1617-1631},
publisher = {Association des Annales de l’institut Fourier},
title = {Dimension of the harmonic measure of non-homogeneous Cantor sets},
url = {http://eudml.org/doc/10186},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Batakis, Athanasios
TI - Dimension of the harmonic measure of non-homogeneous Cantor sets
JO - Annales de l’institut Fourier
PY - 2006
PB - Association des Annales de l’institut Fourier
VL - 56
IS - 6
SP - 1617
EP - 1631
AB - We prove that the dimension of the harmonic measure of the complementary of a translation-invariant type of Cantor sets is a continuous function of the parameters determining these sets. This results extends a previous one of the author and do not use ergotic theoretic tools, not applicables to our case.
LA - eng
KW - Harmonic measure; Cantor sets; fractals; Hausdorff dimension; entropy; harmonic measure; Cantor set; exact measure; code space
UR - http://eudml.org/doc/10186
ER -

References

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