Multifractal analysis for the pointwise Assouad dimension of self-similar measures

Autor:	Anttila, Roope, Suomala, Ville
Rok vydání:	2024
Předmět:	Mathematics - Dynamical Systems Mathematics - Classical Analysis and ODEs 28A80 (Primary) 37C45 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We quantify the pointwise doubling properties of self-similar measures using the notion of pointwise Assouad dimension. We show that all self-similar measures satisfying the open set condition are pointwise doubling in a set of full Hausdorff dimension, despite the fact that they can in general be non-doubling in a set of full Hausdorff measure. More generally, we carry out multifractal analysis by determining the Hausdorff dimension of the level sets of the pointwise Assouad dimension. Comment: 22 pages, 1 figure. Comments are welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2401.03953 Zobrazit plný text záznamu View this record from Arxiv