Dimension of the harmonic measure of non-homogeneous Cantor sets
[Dimension de la mesure harmonique d’ensembles de Cantor non-homogènes]
Batakis, Athanasios
Annales de l'Institut Fourier, Tome 56 (2006), p. 1617-1631 / Harvested from Numdam
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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.

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.

Publié le : 2006-01-01
DOI : https://doi.org/10.5802/aif.2222
Classification:  31A15,  28A80
Mots clés: Mesure Harmonique, Ensembles de Cantor, fractals, Dimension de Hausdorff, Entropie 
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     title = {Dimension of the harmonic measure of non-homogeneous Cantor sets},
     journal = {Annales de l'Institut Fourier},
     volume = {56},
     year = {2006},
     pages = {1617-1631},
     doi = {10.5802/aif.2222},
     zbl = {1113.31001},
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     language = {en},
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Batakis, Athanasios. Dimension of the harmonic measure of non-homogeneous Cantor sets. Annales de l'Institut Fourier, Tome 56 (2006) pp. 1617-1631. doi : 10.5802/aif.2222. http://gdmltest.u-ga.fr/item/AIF_2006__56_6_1617_0/

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