Add to ORKGWe present an algorithm to compute the exact value of the packing measure of self-similar sets satisfying the so called SSC and prove its convergence to the value of the packing measure. We also test the al-gorithm with examples that show both, the accuracy of the algorithm for the most regular cases and the possibility of using the additional information provided by it to obtain formulas for the packing measure of certain self-similar sets. For example, we are able to obtain a for-mula for the packing measure of any Sierpinski gasket with contractio factor in the interval (0, 1/3] (Theorem 2). 1 a
In the context of fractal geometry, the natural extension of volume in Euclidean space is given by H...
Let K be the attractor of a linear iterated function system Sjx = ρjx+bj (j = 1,..., m) on the real ...
AbstractLet μ be a self-similar measure in Rd. A point x∈Rd for which the limit limr↘0logμB(x,r)logr...
We show that the s-dimensional packing measure P^{s}(S) of the Sierpinski gasket S, where s=((log3)/...
In this paper we obtain the rates of convergence of the algorithms given in [13] and [14] for an aut...
A contractive similarity is a function which preserves the geometry of a object but shrinks it down ...
We analyze the local bahaviour of the Hausdorff measure and the packing measure of self-similar sets...
Self-similar measures can be obtained by regarding the self similar set generated by a system of sim...
AbstractWe prove that if a self-similar set E in Rn with Hausdorff dimension s satisfies the strong ...
Let N be an integer with N >= 2 and let X be a compact subset of R-d. If S = (S-1, ..., S-N) is a...
We compute the exact Hausdorff and Packing measures of linear Cantor sets which might not be self si...
Let K be a compact subset ofRn, 0 6 s 6 n. Let P s0, Ps denote s-dimensional packing premeasure and ...
We study sets of local dimensions for self-similar measures in R satisfying the finite neighbour con...
AbstractRecently, Barreira and Schmeling (2000) [1] and Chen and Xiong (1999) [2] have shown, that f...
We study the geometric properties of random multiplicative cascade measures defined on self-similar ...
In the context of fractal geometry, the natural extension of volume in Euclidean space is given by H...
Let K be the attractor of a linear iterated function system Sjx = ρjx+bj (j = 1,..., m) on the real ...
AbstractLet μ be a self-similar measure in Rd. A point x∈Rd for which the limit limr↘0logμB(x,r)logr...
We show that the s-dimensional packing measure P^{s}(S) of the Sierpinski gasket S, where s=((log3)/...
In this paper we obtain the rates of convergence of the algorithms given in [13] and [14] for an aut...
A contractive similarity is a function which preserves the geometry of a object but shrinks it down ...
We analyze the local bahaviour of the Hausdorff measure and the packing measure of self-similar sets...
Self-similar measures can be obtained by regarding the self similar set generated by a system of sim...
AbstractWe prove that if a self-similar set E in Rn with Hausdorff dimension s satisfies the strong ...
Let N be an integer with N >= 2 and let X be a compact subset of R-d. If S = (S-1, ..., S-N) is a...
We compute the exact Hausdorff and Packing measures of linear Cantor sets which might not be self si...
Let K be a compact subset ofRn, 0 6 s 6 n. Let P s0, Ps denote s-dimensional packing premeasure and ...
We study sets of local dimensions for self-similar measures in R satisfying the finite neighbour con...
AbstractRecently, Barreira and Schmeling (2000) [1] and Chen and Xiong (1999) [2] have shown, that f...
We study the geometric properties of random multiplicative cascade measures defined on self-similar ...
In the context of fractal geometry, the natural extension of volume in Euclidean space is given by H...
Let K be the attractor of a linear iterated function system Sjx = ρjx+bj (j = 1,..., m) on the real ...
AbstractLet μ be a self-similar measure in Rd. A point x∈Rd for which the limit limr↘0logμB(x,r)logr...