Hausdorff and harmonic measures on non-homogeneous Cantor sets

Athanasios Batakis (1) , Anna Zdunik (2)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 Institute of Mathematics [Warsaw]

We consider (not self-similar) Cantor sets defined by a sequence of piecewise linear functions. We prove that the dimension of the harmonic measure on such a set is strictly smaller than its Hausdorff dimension. Some Hausdorff measure estimates for these sets are also provided.

Mots clés: Harmonic Measure; fractals; Hausdorff dimension; Cantor sets

Domaines: Analyse classique [math.CA]; Systèmes dynamiques [math.DS]

Athanasios Batakis, Anna Zdunik. Hausdorff and harmonic measures on non-homogeneous Cantor sets. Annales Academiae Scientiarum Fennicae. Mathematica, 2015, pp.40. ⟨hal-00801792⟩