Results 11 to 20 of about 2,785 (188)
Sixty Years of Fractal Projections [PDF]
, 2014 Sixty years ago, John Marstrand published a paper which, among other things, relates the Hausdorff dimension of a plane set to the dimensions of its orthogonal projections onto lines. For many years, the paper attracted very little attention.
A. Ferguson +60 more
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A note on the 1-prevalence of continuous images with full Hausdorff dimension [PDF]
, 2014 We consider the Banach space consisting of real-valued continuous functions on an arbitrary compact metric space. It is known that for a prevalent (in the sense of Hunt, Sauer and Yorke) set of functions the Hausdorff dimension of the image is as large ...
Fraser, Jonathan M., Hyde, James T.
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On random fractals with infinite branching: definition, measurability, dimensions [PDF]
, 2013 We discuss the definition and measurability questions of random fractals and find under certain conditions a formula for upper and lower Minkowski dimensions.
Berlinkov, Artemi
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Assouad type dimensions and homogeneity of fractals [PDF]
, 2013 We investigate several aspects of the Assouad dimension and the lower dimension, which together form a natural `dimension pair'. In particular, we compute these dimensions for certain classes of self-affine sets and quasi-self-similar sets and study ...
Fraser, Jonathan M.
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Dimension bounds for invariant measures of bi-Lipschitz iterated function systems [PDF]
, 2015 We study probabilistic iterated function systems (IFS), consisting of a finite or infinite number of average-contracting bi-Lipschitz maps on R^d. If our strong open set condition is also satisfied, we show that both upper and lower bounds for the ...
Anckar, Andreas
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On the study of multifractal analysis of functions in a metric space
AIMS MathematicsMulti-fractal analysis plays a crucial role in understanding the complex behaviors of functions across different fields. In this study, we presented an innovative approach to examining the multi-fractal formalism.
Amal Mahjoub, Najmeddine Attia
doaj +1 more source
Свойство выпуклости взаимных мультифрактальных размерностей [PDF]
Проблемы анализа, 2010 В работе установлено свойство выпуклости взаимной мультифрактальной упаковочной размерности подмножества пересечения носителей вероятностных борелевских мер μ и v.
Светова Н. Ю.
doaj
Hausdorff dimension of affine random covering sets in torus [PDF]
, 2013 We calculate the almost sure Hausdorff dimension of the random covering set $\limsup_{n\to\infty}(g_n + \xi_n)$ in $d$-dimensional torus $\mathbb T^d$, where the sets $g_n\subset\mathbb T^d$ are parallelepipeds, or more generally, linear images of a set ...
Järvenpää, Esa +4 more
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On distance sets, box-counting and Ahlfors-regular sets [PDF]
, 2017 We obtain box-counting estimates for the pinned distance sets of (dense subsets of) planar discrete Ahlfors-regular sets of exponent $s>1$. As a corollary, we improve upon a recent result of Orponen, by showing that if $A$ is Ahlfors-regular of dimension
Shmerkin, Pablo
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Apollonian circle packings: Dynamics and Number theory [PDF]
, 2014 We give an overview of various counting problems for Apollonian circle packings, which turn out to be related to problems in dynamics and number theory for thin groups.
Oh, Hee
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