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Assouad dimension

In mathematics — specifically, in fractal geometry — the Assouad dimension is a definition of fractal dimension for subsets of a metric space. It was… Expand
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Papers overview

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2018
2018
In analogy with the lower Assouad dimensions of a set, we study the lower Assouad dimensions of a measure. As with the upper… Expand
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2018
2018
JMF was financially supported by the EPSRC grant EP/J013560/1 whilst employed at the University of Warwick. JJM was partially… Expand
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2017
2017
It is shown that for controlled Moran constructions in $\mathbb{R}$, including the (sub) self-similar and more generally, (sub… Expand
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2015
2015
We consider dimensional properties of limit sets of Moran constructions satisfy- ing the finite clustering property. Just to name… Expand
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Highly Cited
2013
Highly Cited
2013
We investigate several aspects of the Assouad dimension and the lower dimension, which together form a natural ‘dimension pair… Expand
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2008
2008
We show that the type function of a space with finite asymptotic dimension estimates its Hilbert (or any $l^p$) compression. The… Expand
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2006
2006
In the first part of the paper we show how to relate several dimension theories (asymptotic dimension with Higson property… Expand
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2005
2005
Let α ≥ 1 and let (X, d, μ) be an α-homogeneous metric measure space with conformal Assouad dimension equal to α. Then there… Expand
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2001
2001
We study the relationship between the Assouad dimension and quasisymmetric mappings, showing that spaces of dimension strictly… Expand
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Highly Cited
1998
Highly Cited
1998
We prove that a non-empty separable metrizable space X admits a totally bounded metric for which the metric dimension of X in… Expand
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