Self-affine examples with interesting properties
The geometry of self affine fractals
... fractal’s properties, see [11, 60, 61, 62, 63, 64, 49] for some ...Since self-affine sets with exceptionally small dimension occur when the iterated components resonate in some way, saying that the ...
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Generating Self-Affine Tiles and Their Boundaries »
... Many of the examples we have seen are tiles which are topological disks. When this is the case, we might try to approximate the boundary with a polygon and feed this result to the ShowIFS command. Let us ...
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On partitioning multivariate self-affine time series
... with large systems, such guesses may be impossible. If we look at the results as represented in the two figures without any prior knowledge, several observations can nonetheless be made regarding the representative ...
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Self affine sets with positive Lebesgue measure
... a n β −n = x. This definition can be extended to β > 2 by letting the digits a n come from a larger digit set. For typical x the β-expansion of x is not unique, indeed almost every x ∈ [ β−1 −1 , β−1 1 ] has uncountably ...
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On the dimensions of a family of overlapping self affine carpets
... Another interesting direction for further work would be to consider self-affine measures sup- ported on our ...of self-affine measures, the proof of Theorem ...
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The Assouad dimension of self affine carpets with no grid structure
... be interesting to push this work further and, in particular, to consider more general families of self-affine carpets, such as those considered by Feng and Wang ...defining affine maps were ...
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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 and fractal constructions based on self affine carpets
... are self-similar sets which no longer need to satisfy the ...is interesting to note that Bedford-McMullen obtained an explicit formula for the Hausdorff dimension, whereas in the other classes the Hausdorff ...
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Interesting Properties of strongly p*gα Connected Spaces and Compact Spaces
... B. In other words, a subset S cannot be expressed as the union of two non-empty strongly p*gαseparated sets A, B. Remark 4.8.For a space (X,τ), every strongly p*gαconnected set is connected (resp.GO-connected) , but the ...
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The Hausdorff and dynamical dimensions of self-affine sponges : a dimension gap result
... 1 Introduction A fundamental question in dynamics is to find “natural” invariant measures on the phase space of a dynamical system. Such measures afford a window into the dynamical complexity of chaotic systems by ...
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Badly approximable points on self-affine sponges and the lower Assouad dimension
... a self-affine sponge, we would like to know what the Hausdorff dimension of its intersection with BA d ...a self-affine sponge intersects BA d ...of self- conformal sets, the answer has ...
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Planar self affine sets with equal Hausdorff, box and affinity dimensions
... with properties of the Furstenberg mea- sure we obtain conditions under which certain classes of plane self-affine sets have Hausdorff or box-counting dimensions equal to their affinity ...of ...
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Badly approximable points on self-affine sponges and the lower Assouad dimension
... 2. Schmidt’s game, hyperplane diffuse sets, and the lower Assouad dimension For d ≥ 2, the full dimension of BA d in R d was proven by Schmidt [24] using a technique now known as Schmidt’s game. Since then, Schmidt’s ...
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The scenery flow for self affine measures
... much interesting dynamics associated to self-affine sets and measures which is not present in the self-similar ...a self-affine set give rise to further iterated function systems ...
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Some Properties and Regions of Variability of Affine Harmonic Mappings and Affine Biharmonic Mappings
... We first obtain the relations of local univalency, convexity, and linear connectedness between analytic functions and their corresponding a ffi ne harmonic mappings.. In addition, the pape[r] ...
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Dimension theory of random self similar and self affine constructions
... that self-similar and self-conformal attractors have finite Hausdorff measure and Hausdorff, packing and box-counting dimensions ...∞-variable self-similar random graph directed constructions we will ...
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Fluid Properties Examples
... A rectangular reservoir with vertical walls has a plan area of 60000m 2. Discharge from the reservoir take place over a rectangular weir. The flow characteristics of the weir is Q = 0.6[r] ...
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On the Lq spectrum of planar self affine measures
... planar self-affine multifractal ...box-like self-affine sets, introduced by the author, which are the attractors of iterated function systems consisting of contracting affine maps which ...
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Ergodicity properties of affine term structure models and applications
... basic affine jump diffusion process (BAJD) and in which the Lévy process takes the form of a com- pound Poisson process with exponentially distributed ...regular affine processes was given in [9]. During ...
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Recurrence to shrinking targets on typical self-affine fractals
... arXiv:1409.7593v2 [math.DS] 19 Oct 2015 TYPICAL SELF-AFFINE FRACTALS HENNA KOIVUSALO AND FELIPE A. RAM´IREZ Abstract. We explore the problem of finding the Hausdorff di- mension of the set of points that ...
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