Work

Non-affine fractal hypersurfaces: construction and dimensions

Year: 2025

Type: article

Abstract: This article presents the construction of a non-affine hypersurface on an n -simplex in \mathbb{R}^{n} . Additionally, fractal dimension of the graph of a non-affine multivariate real-valued fractal function is estimated under certain conditions. Furthermore, the upper bound of the Hausdorff dimension of the invariant probability measure supported on the graph of such fractal function is estimated.

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

DOI: 10.4171/jfg/166

Authors: Alamgir Hossain, Jorge Buescu

Institutions: Presidency University, University of Lisbon

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Presidency University, Fundação para a Ciência e a Tecnologia

Award: Centro de Matemática, Aplicações Fundamentais e Investigação Operacional