Self-affine
The geometry of self affine fractals
... Formulae giving the Hausdorff and box-counting dimensions of self-similar sets satisfying the open set condition are well-known, see Section 1.3. However, cal- culation of the dimensions of general ...
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Dimensions of equilibrium measures on a class of planar self affine sets
... In this paper we consider a natural class of measures which are not quasi-Bernoulli and prove that they satisfy the appropriate version of the Ledrappier-Young formula. One of our main tools, which may be of independent ...
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On The Lq dimensions of measures on Heuter Lalley type self affine sets
... of self- affine sets studied by Hueter and Lalley, the IFS on projective space satisfies the appropriate version of strong separation (S) which renders γ = ...
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Planar self affine sets with equal Hausdorff, box and affinity dimensions
... plane self-affine sets have Hausdorff or box-counting dimensions equal to their affinity ...of self-affine sets for which these dimensions are ...
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Dimension theory and fractal constructions based on self affine carpets
... (either vertical or horizontal, depending on the relative size of c and d). It is interesting to note that one cannot approximate the box and packing dimensions ‘from within’ in the same way. To see this observe that in ...
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Recurrence to shrinking targets on typical self-affine fractals
... to self- affine sets does not necessarily coincide with the classical one, under the assumption (6) the measure µ satisfies the Facts 1-3 in Section 3 of ...
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Recurrence to shrinking targets on typical self-affine fractals
... to self- affine sets does not necessarily coincide with the classical one, under the assumption (6) the measure µ satisfies the Facts 1-3 in Section 3 of ...
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The Assouad dimension of self affine carpets with no grid structure
... sometimes referred to as the rectangular open set condition. Often one requires additional conditions on the defining IFS in order to obtain explicit dimension formulae. One such condition which is particularly relevant ...
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Self-affine subglacial roughness : Consequences for radar scattering and basal water discrimination in northern Greenland
... exhibits self-affine (power law) roughness scaling behaviour, but existing radar scattering models do not take this into ...a self-affine statistical frame- work that enables a consistent ...
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Analysis of the geomagnetic activity of the D(st) index and self-affine fractals using wavelet transforms
... The physical features of a dynamic system can be easily de- tected and revealed using frequency domain analysis, which is often implemented by means of Fourier transforms of the covariance functions. One feature of a ...
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The Hausdorff and dynamical dimensions of self-affine sponges : a dimension gap result
... of affine iterated function systems whose contractions preserve the class of coordinate-parallel rectangles, see ...matrix. Self-affine sets resulting from these “coordinate-permuting IFSes” are ...
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Digit frequencies and self affine sets with non empty interior
... planar self-affine sets we show that if the horizontal contraction lies in a certain parameter space and the vertical contractions are sufficiently close to 1, then every nontrivial vertical fibre contains ...
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Dimension theory of random self similar and self affine constructions
... generated from a single IFS with randomly chosen translation vectors and showed that the Hausdorff dimension coincides almost surely (with respect to the chosen transla- tion vectors) with the ‘affinity dimension’. The ...
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Generating Self-Affine Tiles and Their Boundaries »
... the self-affine tiles . A tile T is self-affine if there is an expanding matrix A and a collection of vectors (called the digit set ) such ...
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On the Lq spectrum of planar self affine measures
... studying self-affine sets and measures, beginning in the 1980s with the seminal works on what became known as self-affine carpets by Bedford [Be] and McMullen [M] and the general case studied ...
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On the dimensions of a family of overlapping self affine carpets
... This set F is called the attractor of the IFS and this class of attractors was first studied in the mid-eighties independently by Bedford [4] and McMullen [23], who each gave a formula for the Hausdorff and box ...
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The scenery flow for self affine measures
... non-overlapping self-similar and self-conformal measures is well understood, [4, 5, 12, ...the self-affine setting, the scenery flow has previously been studied for measures on ...
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The effect of self affine fractal roughness of wires on atom chips
... We have examined how a magnetic trap formed by a current-carrying wire is sensitive to the roughness on the edges of the wire. In particular, we have extended previous discussions to consider the case of a ...
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Singularity and similarity detection for signals using the wavelet transform
... a self-affine time series is that the power spectral density of the time series has a power-law dependence on ...a self-affine time series is that the power spectral density of the time series ...
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Restrictions of holder continuous functions
... and upper Minkowski dimension, respectively. The upper bound on V (α) is a consequence of the following theorem. Let {B(t) : t ∈ [0, 1]} be a fractional Brownian motion of Hurst index α. Then, almost surely, there exists ...
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