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.
Nous montrons que la dimension de la mesure harmonique du complémentaire d’ensembles de Cantor de type invariant par translation est une fonction continue des paramètres définissant ces ensembles. Ce résultat prolonge un précédent du même auteur et n’implique pas d’outils de la théorie ergotique, non-applicables dans notre configuration.
Keywords: Harmonic measure, Cantor sets, fractals, Hausdorff dimension, entropy
Mot clés : Mesure Harmonique, Ensembles de Cantor, fractals, Dimension de Hausdorff, Entropie
@article{AIF_2006__56_6_1617_0, author = {Batakis, Athanasios}, title = {Dimension of the harmonic measure of non-homogeneous {Cantor} sets}, journal = {Annales de l'Institut Fourier}, pages = {1617--1631}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {56}, number = {6}, year = {2006}, doi = {10.5802/aif.2222}, zbl = {1113.31001}, mrnumber = {2282670}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2222/} }
TY - JOUR AU - Batakis, Athanasios TI - Dimension of the harmonic measure of non-homogeneous Cantor sets JO - Annales de l'Institut Fourier PY - 2006 SP - 1617 EP - 1631 VL - 56 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2222/ DO - 10.5802/aif.2222 LA - en ID - AIF_2006__56_6_1617_0 ER -
%0 Journal Article %A Batakis, Athanasios %T Dimension of the harmonic measure of non-homogeneous Cantor sets %J Annales de l'Institut Fourier %D 2006 %P 1617-1631 %V 56 %N 6 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2222/ %R 10.5802/aif.2222 %G en %F AIF_2006__56_6_1617_0
Batakis, Athanasios. Dimension of the harmonic measure of non-homogeneous Cantor sets. Annales de l'Institut Fourier, Volume 56 (2006) no. 6, pp. 1617-1631. doi : 10.5802/aif.2222. http://archive.numdam.org/articles/10.5802/aif.2222/
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