Work

Local dimension spectrum for dominated planar self-affine sets

Year: 2026

Type: article

Abstract: The local dimension spectrum provides a framework for quantifying the fractal properties of a measure, and it is well understood for non-overlapping self-similar measures. In this article, we study the local dimension spectrum for dominated self-affine measures. By analyzing exact dimensionality, we obtain deterministic results that extend the scope of the local dimension spectrum beyond the almost-sure setting.

Source: Mathematische Zeitschrift

DOI: 10.1007/s00209-026-03972-2

Authors: Alex Batsis, Antti Käenmäki, Tom Kempton

Institutions: University of Manchester, University of Eastern Finland

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: Itä-Suomen Yliopisto, Kuopion Yliopistollinen Sairaala