Work

An Improved Fractal Analysis of Directional Densities for Borel Probability Measures

Year: 2026

Type: article

Abstract: We investigate pointwise rectangular anisotropic and directional densities for Borel probability measures with compact support. Contrary to traditional densities, these new notions have the advantage to weight the side lengths of local boxes differently and take into account long thin boxes. We employ similarities with statistical physics to extract interesting multifractal information using the Hausdorff dimension with respect to the coverings by rectangles with small enough Lebesgue measure (instead of requiring all side lengths to be small). We apply our analysis for invariant measures for some iterated function systems.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract10110760

Authors: Ines Ben Omrane, Abdulmajeed Alqasem, Mourad Ben Slimane, Hamdi Zorgati

Institutions: Imam Mohammad ibn Saud Islamic University, King Saud University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,258

Funder: King Saud University