Work

Critical values for intermediate and box dimensions of projections and other images of compact sets

Year: 2025

Type: article

Abstract: Given a compact set E \subset \mathbb{R}^{d} , we investigate for which values of m the equality \operatorname{dim}_{\theta} P_{V}(E) = m or \operatorname{dim}_{\theta} P_{V}(E) = \operatorname{dim}_{\theta} E holds for \gamma_{d,m} -almost all V \in G(d,m) . Our result extends to more general functions, including orthogonal projections and fractional Brownian motion. As a particular case, when \theta = 1 , the results apply to the box dimension.

Source: Journal of Fractal Geometry Mathematics of Fractals and Related Topics

DOI: 10.4171/jfg/168

Authors: Nicolas Angelini, Ursula Maria Molter

Institutions: National University of San Luis, Consejo Nacional de Investigaciones Científicas y Técnicas, Universidad de Buenos Aires

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Consejo Nacional de Investigaciones Científicas y Técnicas, Secretaría de Ciencia y Técnica, Universidad de Buenos Aires

OpenAlex ID: W4411432816

FWCI: 4.824

Cites:

Cited by: 3

Related to: 10