Dimensions of harmonic measures on non-autonomous Cantor sets - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

Dimensions of harmonic measures on non-autonomous Cantor sets

Athanasios Batakis

Résumé

We consider Non Autonomous Conformal Iterative Function Systems (NACIFS)and their limit set. Our main concern is harmonic measure and its dimensions : Haus-dorff and Packing. We prove that this two dimensions are continuous under perturba-tions and that they verify Bowen’s and Manning’s type formulas. In order to do so weprove general results about measures, and more generally about positive functionals,defined on a symbolic space, developing tools from thermodynamical formalism in anon-autonomous setting.
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Dates et versions

hal-04690558 , version 1 (06-09-2024)

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  • HAL Id : hal-04690558 , version 1

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Athanasios Batakis, Guillaume Havard. Dimensions of harmonic measures on non-autonomous Cantor sets. 2024. ⟨hal-04690558⟩
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