Dimension of the harmonic measure of non-homogeneous Cantor sets
Annales de l'Institut Fourier, Volume 56 (2006) no. 6, pp. 1617-1631.

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.

DOI: 10.5802/aif.2222
Classification: 31A15, 28A80
Keywords: Harmonic measure, Cantor sets, fractals, Hausdorff dimension, entropy
Batakis, Athanasios 1

1 Université d’Orléans Département de Mathématiques MAPMO BP 6759 45067 Orléans cedex 2 (France)
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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. https://aif.centre-mersenne.org/articles/10.5802/aif.2222/

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