Fractal dimension for fractal structures: a Hausdorff approach revisited

DOI10.1016/J.JMAA.2013.07.011zbMath1309.28003OpenAlexW2016119108MaRDI QIDQ2258972

Manuel Fernández-Martínez, Miguel Angel Sánchez-Granero

Publication date: 27 February 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2013.07.011

zbMATH Keywords

Hausdorff dimensionHausdorff measurefractal dimensionbox-counting dimensionfractalfractal structuregeneralized fractal space

Mathematics Subject Classification ID

Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Fractals (28A80) Hausdorff and packing measures (28A78)

Related Items (12)

A new fractal dimension for curves based on fractal structures ⋮ Fractal dimension for IFS-attractors revisited ⋮ A new topological indicator for chaos in mechanical systems ⋮ How to calculate the Hausdorff dimension using fractal structures ⋮ A survey on fractal dimension for fractal structures ⋮ Irreducible fractal structures for Moran type theorems ⋮ Counterexamples in theory of fractal dimension for fractal structures ⋮ On discrete models of fractal dimension to explore the complexity of discrete dynamical systems ⋮ Fractal and Hausdorff dimensions for systems of iterative functional equations ⋮ Calculating Hausdorff dimension in higher dimensional spaces ⋮ Theoretical properties of fractal dimensions for fractal structures ⋮ Generating pre-fractals to approach real IFS-attractors with a fixed Hausdorff dimension

Cites Work

• Fractal dimension for fractal structures
• Fractal dimension for fractal structures: A Hausdorff approach
• Classification of Moran fractals
• Scale relativity and fractal space-time: applications to quantum physics, cosmology and chaotic systems.
• Exponential attractor and its fractal dimension for a second order lattice dynamical system
• A new method of estimation of the box-counting dimension of multivariate objects using space-filling curves
• The Hausdorff dimension of a class of recurrent sets
• Fractal dimension for fractal structures: applications to the domain of words
• A variational principle for fractal dimensions
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