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Hausdorff and Packing Measures of the Level Sets of Iterated Brownian Motion
Journal of Theoretical Probability, 1999Iterated Brownian motion is defined as \(Z(t)=X(Y(t))\) where \(X\) and \(Y\) are independent (two-sided) Brownian motions. The exact Hausdorff dimension gauge of the level sets of iterated Bronwian motion is determined to be \(\varphi(x)=x^{3/4}[\log\log(1/x)]^{3/4}\). This result generalizes earlier work of \textit{K.
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Chaos, Solitons & Fractals, 2005
The authors establish Frostman-type lemmas for the Hausdorff and pre-packing measures on a product probability measure space \((\Omega, {\mathcal F}, \mu) = (\Omega_1\times \Omega_2, {\mathcal F}_1\times {\mathcal F}_2, \mu_1\times\mu_2)\). Based on these results, they prove a sufficient condition for the Hausdorff and packing dimensions with respect ...
Dai, Chaoshou, Hou, Yanyan
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The authors establish Frostman-type lemmas for the Hausdorff and pre-packing measures on a product probability measure space \((\Omega, {\mathcal F}, \mu) = (\Omega_1\times \Omega_2, {\mathcal F}_1\times {\mathcal F}_2, \mu_1\times\mu_2)\). Based on these results, they prove a sufficient condition for the Hausdorff and packing dimensions with respect ...
Dai, Chaoshou, Hou, Yanyan
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Upper and Lower Densities of Measures and Comparison with Hausdorff and Packing Measures
Fractals and Dynamics in Mathematics, Science and the Artsopenaire +3 more sources
Nonlinearity, 2008
In this work, we focus on the multifractal centred Hausdorff measure and the multifractal packing measure in . We find that for 0 < s < t < 2, q < 1, then there exist a set and a probability measure μ on such that and, in addition,
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In this work, we focus on the multifractal centred Hausdorff measure and the multifractal packing measure in . We find that for 0 < s < t < 2, q < 1, then there exist a set and a probability measure μ on such that and, in addition,
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The branching measure, Hausdorff and packing measures on the Galton-Watson tree
2000We present some recent results concerning the branching measure, the exact Husdorff measure and the exact packing measure, defined on the boundary of the Caalton-Watson tree. The results show that in good cases, these three measures coincide each other up to a constant, that the branching measure is homogeneous (it has the same local dimension at each ...
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Hausdorff and packing dimensions, intersection measures, and similarities
1999Let \(\mu\) and \(\nu\) be Radon measures on \(\mathbb R^n\) with compact supports. We study the Hausdorff, \(\dim_H\), and packing dimension, \(\dim_p\), properties of the intersection measures \(\mu\cap f_\sharp\nu\) when \(f\) runs through the similarities of \(\mathbb R^n\) and \(f_\sharp\nu\) is the image of \(\nu\) under \(f\). These measures can
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Commentationes Mathematicae Universitatis Carolinae, 2009
Summary: We extend the notions of Hausdorff and packing dimension introducing weights in their definition. These dimensions are computed for ergodic invariant probability measures of two-dimensional Lorenz transformations, which are transformations of the type occuring as first return maps to a certain cross section for the Lorenz differential equation.
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Summary: We extend the notions of Hausdorff and packing dimension introducing weights in their definition. These dimensions are computed for ergodic invariant probability measures of two-dimensional Lorenz transformations, which are transformations of the type occuring as first return maps to a certain cross section for the Lorenz differential equation.
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Regularities of general Hausdorff and packing functions
Chaos, Solitons and Fractals, 2019Zied Douzi, Bilel Selmi
exaly