A relative multifractal analysis: box-dimensions, densities, and projections
Zied Douzi, Bilel Selmi
Abstract
We are interested in the behavior of relative multifractal box-dimensions, density results and multifractal dimensions under projections onto a lower-dimensional linear subspace. The results in this paper establish the connections with various multifractal and fractal dimensions and their projections, and generalize many known results about Hausdorff and packing measures and dimensions of a subset of ℝn.
Topics & Concepts
Multifractal systemMathematicsHausdorff dimensionFractalBox countingSubspace topologyHausdorff spaceFractal dimensionPacking dimensionStatistical physicsCombinatoricsFractal analysisMathematical analysisMinkowski–Bouligand dimensionPhysicsMathematical Dynamics and FractalsAdvanced Mathematical Theories and ApplicationsTheoretical and Computational Physics