Work

Hausdorff dimension of self-similar measures and sets with common fixed-point structure

Year: 2026

Type: article

Abstract: In this paper, we study the Hausdorff dimension of self-similar measures and sets on the real line, where the generating iterated function system consists of maps that share a common fixed point. In particular, we show that out of a Hausdorff codimension-one exceptional set of natural parameters, such systems satisfy a weak exponential separation. This significantly strengthens the previous result of Bárány and Szvák [On the dimension of self-similar measures with complicated overlaps. Math. Nachr. 294 (4) (2021), 657–671]. As an application, we give the Hausdorff dimension of self-affine measures supported on the generalized 4-corner set.

Source: Ergodic Theory and Dynamical Systems

DOI: 10.1017/etds.2026.10342

Authors: BALÁZS BÁRÁNY, MANUJ VERMA

Institution: Budapest University of Technology and Economics

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Nemzeti Kutatási, Fejlesztési és Innovaciós Alap

Award: G9000386104