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Hausdorff Dimension
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Recent papers in Hausdorff Dimension
En diversos países pequeños grupos de arqueólogos se han lanzado a utilizar medidas de dimensión fractal aplicadas a distintas clases de objetos, desde ornamentación cerámica a motivos de bordados, desde plantas urbanas a edificios. Una... more
In this paper, we provide the first known overall algorithm to calculate the Hausdorff dimension of any compact Euclidean subset. This novel approach is based on both a new discrete model of fractal dimension for a fractal structure which... more
We propose a model for a power-counting renormalizable field theory living in a fractal spacetime. The action is Lorentz covariant and equipped with a Stieltjes measure. The system flows, even in a classical sense, from an ultraviolet... more
This paper explores the working hypothesis that fractal patterns that closely match those found in nature are more likely to convey a strong sense of genius loci to humans by comparison with 'Euclidean' patterns that do not occur in... more
This paper provides a new model to compute the fractal dimension of a subset on a generalized-fractal space. Recall that fractal structures are a perfect place where a new definition of fractal dimension can be given, so we perform a... more
Fractal dimension constitutes the main tool to test for fractal patterns in Euclidean contexts. For this purpose, it is always used the box dimension, since it is easy to calculate, though the Hausdorff dimension, which is the oldest and... more
Along the years, the foundations of Fractal Geometry have received contributions starting from mathematicians like Cantor, Peano, Hilbert, Hausdorff, Carathéodory, Sierpi´nski, and Besicovitch, to quote some of them. They were some of the... more
Let $X=\{X(t),t\in\mathbb{R}^N\}$ be a random field with values in $\mathbb{R}^d$. For any finite Borel measure $\mu$ and analytic set $E\subset\mathbb{R}^N$, the Hausdorff and packing dimensions of the image measure $\mu_X$ and image set... more
1. Einleitung zur historischen Neuentwicklung der Chaostheorie 1 2. Die Einschätzung der Bedeutung der Chaostheorie in der wissenschaftlichen... more
Various results are presented here: First, a simple but formal measure-theoretic construction of the derivative is given, making it clear that it has a very concrete existence as a Lebesgue-Stieltjes measure, and thus is safe to... more
This paper examines the pure-strategy subgame-perfect equilibrium payoffs in discounted supergames with perfect monitoring. It is shown that the equilibrium payoffs can be identified as sub-self-affine sets or graph-directed iterated... more
In this paper, we use fractal structures to study a new approach to the Hausdorff dimension from both continuous and discrete points of view. We show that it is possible to generalize the Hausdorff dimension in the context of Euclidean... more
The three-dimensional Navier-Stokes-α model for fast rotating geophysical fluids is considered. The Navier-Stokes-α model is a nonlinear dispersive regularization of the exact Navier-Stokes equations obtained by Lagrangian averaging and... more
1 Department of Mathematics, PennState University, University Park, Pennsylvania 16802; e-mail: dolgop@math.psu.edu 2 Department of Mathematics, MIT, Cambridge, Massachusetts 02139; e-mail: kaloshin@ math.mit.edu 3 Department of... more
